• 1482 Citations
  • 19 h-Index
1988 …2021
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Research Output 1988 2019

  • 1482 Citations
  • 19 h-Index
  • 75 Article
  • 13 Conference contribution
  • 3 Chapter
  • 1 Comment/debate
2019

An effective Lie–Kolchin Theorem for quasi-unipotent matrices

Koberda, T., Luo, F. & Sun, H., Nov 15 2019, In : Linear Algebra and Its Applications. 581, p. 304-323 20 p.

Research output: Contribution to journalArticle

Jordan Canonical Form
Mapping Class Group
Representation Theory
Theorem
Eigenvalues and eigenfunctions

Author Correction: Community Detection on Networks with Ricci Flow (Scientific Reports, (2019), 9, 1, (9984), 10.1038/s41598-019-46380-9)

Ni, C. C., Lin, Y. Y., Luo, F. & Gao, J., Dec 1 2019, In : Scientific reports. 9, 1, 12870.

Research output: Contribution to journalComment/debate

Open Access
1 Citation (Scopus)

Community Detection on Networks with Ricci Flow

Ni, C. C., Lin, Y. Y., Luo, F. & Gao, J., Dec 1 2019, In : Scientific reports. 9, 1, 9984.

Research output: Contribution to journalArticle

Open Access
Community Networks
Mathematics

Convergence of discrete conformal geometry and computation of uniformization maps

Gu, D., Luo, F. & Wu, T., Jan 1 2019, In : Asian Journal of Mathematics. 23, 1, p. 21-34 14 p.

Research output: Contribution to journalArticle

Conformal Geometry
Discrete Geometry
Uniformization
Geometry
Riemannian Metric
2018
11 Citations (Scopus)

A discrete uniformization theorem for polyhedral surfaces

Gu, X. D., Luo, F., Sun, J. & Wu, T., Jun 1 2018, In : Journal of Differential Geometry. 109, 2, p. 223-256 34 p.

Research output: Contribution to journalArticle

Uniformization
Metric
Theorem
Curvature
Variational Principle
9 Citations (Scopus)

A discrete uniformization theorem for polyhedral surfaces II

Gu, X., Guo, R., Luo, F., Sun, J. & Wu, T., Jul 2018, In : Journal of Differential Geometry. 109, 3, p. 431-466 36 p.

Research output: Contribution to journalArticle

Uniformization
Metric
Theorem
Discrete Curvature
Hyperbolic Metric
2 Citations (Scopus)

Volume and rigidity of hyperbolic polyhedral 3-manifolds

Luo, F. & Yang, T., Mar 2018, In : Journal of Topology. 11, 1, p. 1-29 29 p.

Research output: Contribution to journalArticle

Rigidity
Metric
Isometry
Curvature
Gluing
2017

A new combinatorial class of 3-manifold triangulations

Luo, F. & Tillmann, S., Jan 1 2017, In : Asian Journal of Mathematics. 21, 3, p. 543-570 28 p.

Research output: Contribution to journalArticle

Triangulation
Topology
Minimality
Circle
Restriction
1 Citation (Scopus)

Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds

Casella, A., Luo, F. & Tillmann, S., Jan 1 2017, In : Proceedings of the American Mathematical Society. 145, 8, p. 3543-3560 18 p.

Research output: Contribution to journalArticle

Triangulation
Cones
Cone
Genus
Parameterization

The riemann mapping theorem and its discrete counterparts

Luo, F., Jan 1 2017, From Riemann to Differential Geometry and Relativity. Springer International Publishing, p. 367-388 22 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Uniformization
Theorem
2016
8 Citations (Scopus)

A TQFT of Turaev–Viro Type on Shaped Triangulations

Kashaev, R., Luo, F. & Vartanov, G., May 1 2016, In : Annales Henri Poincare. 17, 5, p. 1109-1143 35 p.

Research output: Contribution to journalArticle

triangulation
Triangulation
Three-manifolds
Partition Function
Dihedral angle

On a conjecture of milnor about volumes of simplexes

Guo, R. & Luo, F., Jan 1 2016, In : Asian Journal of Mathematics. 20, 5, p. 957-968 12 p.

Research output: Contribution to journalArticle

Gram Matrix
Closure
Angle
17 Citations (Scopus)

Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampere equations

Gu, X., Luo, F., Sun, J. & Yau, S. T., Jan 1 2016, In : Asian Journal of Mathematics. 20, 2, p. 383-398 16 p.

Research output: Contribution to journalArticle

Optimal Transport
Computational geometry
Monge-Ampère Equation
Discrete Equations
Variational Principle
2015
3 Citations (Scopus)

Discrete conformal deformation: Algorithm and experiments

Sun, J., Wu, T., Gu, X. & Luo, F., Jul 14 2015, In : SIAM Journal on Imaging Sciences. 8, 3, p. 1421-1456 36 p.

Research output: Contribution to journalArticle

Conformal Deformation
Curvature
Metric
Experiment
Experiments
23 Citations (Scopus)

Optimal Mass Transport for Shape Matching and Comparison

Su, Z., Wang, Y., Shi, R., Zeng, W., Sun, J., Luo, F. & Gu, X., Nov 1 2015, In : IEEE Transactions on Pattern Analysis and Machine Intelligence. 37, 11, p. 2246-2259 14 p., 7053911.

Research output: Contribution to journalArticle

Optimal Transport
Shape Space
Shape Matching
Mass Transport
Mass transfer
1 Citation (Scopus)

Solving Thurston's equation in a commutative ring

Luo, F., Jul 29 2015, In : Journal of Topology. 9, 1, p. 143-160 18 p., jtv040.

Research output: Contribution to journalArticle

Commutative Ring
Entropy Function
Critical point
7 Citations (Scopus)

Survey on Discrete Surface Ricci Flow

Zhang, M., Zeng, W., Guo, R., Luo, F. & Gu, X. D., May 1 2015, In : Journal of Computer Science and Technology. 30, 3, p. 598-613 16 p.

Research output: Contribution to journalArticle

Ricci Flow
Curvature
Riemannian Metric
Heat Diffusion
Shape Analysis
2014
5 Citations (Scopus)

A dilogarithm identity on moduli spaces of curves

Luo, F. & Tan, S. P., Jun 2014, In : Journal of Differential Geometry. 97, 2, p. 255-274 20 p.

Research output: Contribution to journalArticle

Dilogarithm
Moduli Space of Curves
Hyperbolic Surface
Closed Geodesics
Torus
2 Citations (Scopus)

Optimal mass transport for geometric modeling based on variational principles in convex geometry

Su, Z., Sun, J., Gu, X., Luo, F. & Yau, S. T., Jan 1 2014, In : Engineering with Computers. 30, 4, p. 475-486 12 p.

Research output: Contribution to journalArticle

Convex Geometry
Optimal Transport
Geometric Modeling
Mass Transport
Parameterization
7 Citations (Scopus)

Rigidity of polyhedral surfaces, I

Luo, F., Feb 2014, In : Journal of Differential Geometry. 96, 2, p. 241-302 62 p.

Research output: Contribution to journalArticle

Rigidity
Cosine rule or law of cosines
Variational Approach
Isometry
Variational Principle
17 Citations (Scopus)

The unified discrete surface Ricci flow

Zhang, M., Guo, R., Zeng, W., Luo, F., Yau, S. T. & Gu, X., Sep 2014, In : Graphical Models. 76, 5, p. 321-339 19 p.

Research output: Contribution to journalArticle

Ricci Flow
Circle packing
Curvature
Heat Diffusion
Hessian matrix
2013
40 Citations (Scopus)

Area-preservation mapping using optimal mass transport

Zhao, X., Su, Z., Gu, X. D., Kaufman, A., Sun, J., Gao, J. & Luo, F., Nov 4 2013, In : IEEE Transactions on Visualization and Computer Graphics. 19, 12, p. 2838-2847 10 p., 6634117.

Research output: Contribution to journalArticle

Mass transfer
Visualization
Conformal mapping
Convex optimization
Medical imaging
1 Citation (Scopus)

Geometric registration based on distortion estimation

Zeng, W., Goswami, M., Luo, F. & Gu, X., Jan 1 2013, Proceedings - 2013 IEEE International Conference on Computer Vision, ICCV 2013. Institute of Electrical and Electronics Engineers Inc., p. 2632-2639 8 p. 6751438. (Proceedings of the IEEE International Conference on Computer Vision).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Conformal mapping
Computer vision
Concretes
Experiments
8 Citations (Scopus)

Volume optimization, normal surfaces, and thurston’s equation on triangulated 3-manifolds

Luo, F., Jan 1 2013, In : Journal of Differential Geometry. 93, 2, p. 299-326 28 p.

Research output: Contribution to journalArticle

Normal Surface
Gluing
Optimization
Variational Principle
Critical point
2012
29 Citations (Scopus)

Computing quasiconformal maps using an auxiliary metric and discrete curvature flow

Zeng, W., Lui, L. M., Luo, F., Chan, T. F. C., Yau, S. T. & Gu, D. X., Aug 1 2012, In : Numerische Mathematik. 121, 4, p. 671-703 33 p.

Research output: Contribution to journalArticle

Discrete Curvature
Quasiconformal Maps
Curvature Flow
Metric
Computing
19 Citations (Scopus)

Discrete heat kernel determines discrete Riemannian metric

Zeng, W., Guo, R., Luo, F. & Gu, X., Jul 1 2012, In : Graphical Models. 74, 4, p. 121-129 9 p.

Research output: Contribution to journalArticle

Laplace-Beltrami Operator
Heat Kernel
Riemannian Metric
Cotangent
Triangle Mesh
24 Citations (Scopus)

Numerical computation of surface conformal mappings

Gu, X. D., Zeng, W., Luo, F. & Yau, S. T., Jan 1 2012, In : Computational Methods and Function Theory. 11, 2, p. 747-787 41 p.

Research output: Contribution to journalArticle

Conformal mapping
Conformal Mapping
Numerical Computation
Geometric Analysis
Riemann Surface
12 Citations (Scopus)

Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds

Luo, F., Tillmann, S. & Yang, T., Nov 5 2012, In : Proceedings of the American Mathematical Society. 141, 1, p. 335-350 16 p.

Research output: Contribution to journalArticle

Hyperbolic Structure
Gluing
Hyperbolic 3-manifold
Triangulation
Rigidity
2 Citations (Scopus)

Volume maximization and the extended hyperbolic space

Luo, F. & Schlenker, J. M., Jan 1 2012, In : Proceedings of the American Mathematical Society. 140, 3, p. 1053-1068 16 p.

Research output: Contribution to journalArticle

Hyperbolic Structure
Hyperbolic Space
Hyperbolic Metric
Decomposition
Spacelike Surface
2011
1 Citation (Scopus)

3D surface representation using ricci flow

Zeng, W., Luo, F., Yau, S. T. & Gu, D. X., Jan 1 2011, Computer Vision: From Surfaces to 3D Objects. CRC Press, p. 65-93 29 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Geometry
Topology
3 Citations (Scopus)

Cell decompositions of Teichmüller spaces of surfaces with boundary

Guo, R. & Luo, F., 2011, In : Pacific Journal of Mathematics. 253, 2, p. 423-438 16 p.

Research output: Contribution to journalArticle

Cell Decomposition
Mapping Class Group
Invariant
1 Citation (Scopus)

Computing shortest words via shortest loops on hyperbolic surfaces

Yin, X., Li, Y., Han, W., Luo, F., Gu, X. D. & Yau, S. T., Nov 1 2011, In : CAD Computer Aided Design. 43, 11, p. 1449-1456 8 p.

Research output: Contribution to journalArticle

Computational complexity
22 Citations (Scopus)

Rigidity of polyhedral surfaces, III

Luo, F., Dec 12 2011, In : Geometry and Topology. 15, 4, p. 2299-2319 21 p.

Research output: Contribution to journalArticle

Circle packing
Rigidity
Discrete Curvature
Discrete Laplacian
Metric
2010
6 Citations (Scopus)

Fundamentals of Computational Conformal Geometry

Gu, D. X., Luo, F. & Yau, S. T., Dec 1 2010, In : Mathematics in Computer Science. 4, 4, p. 389-429 41 p.

Research output: Contribution to journalArticle

Conformal Geometry
Computational Geometry
Geometric Analysis
Ricci Flow
Geometry
23 Citations (Scopus)

Parameterization of star-shaped volumes using Green's functions

Xia, J., He, Y., Han, S., Fu, C. W., Luo, F. & Gu, X., Jul 21 2010, Advances in Geometric Modeling and Processing - 6th International Conference, GMP 2010, Proceedings. p. 219-235 17 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6130 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Parameterization
Green's function
Stars
Star
Geometric Design
39 Citations (Scopus)

Resilient routing for sensor networks using hyperbolic embedding of universal covering space

Zeng, W., Sarkar, R., Luo, F., Gu, X. & Gao, J., Jun 15 2010, 2010 Proceedings IEEE INFOCOM. 5461988. (Proceedings - IEEE INFOCOM).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Routing algorithms
Sensor networks
Jamming
Parallel algorithms
Resource allocation

Simple loops on surfaces and their intersection numbers

Luo, F., Jan 1 2010, In : Journal of Differential Geometry. 85, 1, p. 73-115 43 p.

Research output: Contribution to journalArticle

Intersection number
Lamination
Tropical Geometry
Semiring
Compactification
2009
18 Citations (Scopus)

Canonical homotopy class representative using hyperbolic structure

Zeng, W., Jin, M., Luo, F. & Gu, X. D., Nov 20 2009, 2009 IEEE International Conference on Shape Modeling and Applications, SMI 2009. p. 171-178 8 p. 5170145. (2009 IEEE International Conference on Shape Modeling and Applications, SMI 2009).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Topology
Equivalence classes
Pipelines
Decomposition
27 Citations (Scopus)

Computing Teichmüller shape space

Jin, M., Zeng, W., Luo, F. & Gu, X., May 1 2009, In : IEEE Transactions on Visualization and Computer Graphics. 15, 3, p. 504-517 14 p., 4624253.

Research output: Contribution to journalArticle

Topology
Equivalence classes
Computer graphics
Geometry
5 Citations (Scopus)

Discrete curvature flows for surfaces and 3-manifolds

Yin, X., Jin, M., Luo, F. & Gul, X. D., Jul 13 2009, Emerging Trends in Visual Computing - LIX Fall Colloquium, ETVC 2008, Revised Invited Papers. p. 38-74 37 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5416).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Discrete Curvature
Curvature Flow
Medical imaging
Computer graphics
Intrinsic curvature
29 Citations (Scopus)

Generalized discrete Ricci flow

Yang, Y. L., Guo, R., Luo, F., Hu, S. M. & Gu, X., Oct 2009, In : Computer Graphics Forum. 28, 7, p. 2005-2014 10 p.

Research output: Contribution to journalArticle

Triangulation
Parameterization
Topology
Geometry
17 Citations (Scopus)

Generalized Koebe's method for conformal mapping multiply connected domains

Zeng, W., Yin, X., Zhang, M., Luo, F. & Gu, X., Nov 9 2009, Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling. p. 89-100 12 p. 1629267. (Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Multiply Connected Domain
Conformal mapping
Conformal Mapping
Multiplication
Ring or annulus
91 Citations (Scopus)

Greedy routing with guaranteed delivery using Ricci flows

Sarkar, R., Yin, X., Gao, J., Luo, F. & Gu, X. D., Nov 16 2009, 2009 International Conference on Information Processing in Sensor Networks, IPSN 2009. p. 121-132 12 p. 5211935

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Conformal mapping
Triangulation
Sensor nodes
Sensor networks
Wireless sensor networks
1 Citation (Scopus)

Recent advances in computational conformal geometry

Gu, X. D., Luo, F. & Yau, S. T., Oct 16 2009, Mathematics of Surfaces XIII - 13th IMA International Conference, Proceedings. p. 189-221 33 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5654 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Conformal Geometry
Computational Geometry
Triangulation
Geometry
Curvature Flow
21 Citations (Scopus)

Rigidity of polyhedral surfaces, II

Guo, R. & Luo, F., Dec 1 2009, In : Geometry and Topology. 13, 3, p. 1265-1312 48 p.

Research output: Contribution to journalArticle

Cosine rule or law of cosines
Rigidity
Variational Principle
Geodesic
Disjoint
26 Citations (Scopus)

Surface quasi-conformal mapping by solving beltrami equations

Zeng, W., Luo, F., Yau, S. T. & Gu, X. D., Oct 16 2009, Mathematics of Surfaces XIII - 13th IMA International Conference, Proceedings. p. 391-408 18 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5654 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Beltrami Equation
Conformal mapping
Quasiconformal Mapping
Quasiconformal Maps
Conformal Structure
2008
6 Citations (Scopus)

3-dimensional Schläfli formula and its generalization

Luo, F., Nov 1 2008, In : Communications in Contemporary Mathematics. 10, SUPPL. 1, p. 835-842 8 p.

Research output: Contribution to journalArticle

Triangular pyramid
Curvature
Generalization
11 Citations (Scopus)

Angle structures and normal surfaces

Luo, F. & Tillmann, S., Jun 1 2008, In : Transactions of the American Mathematical Society. 360, 6, p. 2849-2866 18 p.

Research output: Contribution to journalArticle

Normal Surface
Triangulation
Angle
Euler Function
Manifolds with Boundary
1 Citation (Scopus)

Comparing corresponding dihedral angles on classical geometric simplices

Au, T. K. K., Luo, F. & Stong, R., Jun 2008, In : Asian Journal of Mathematics. 12, 2, p. 203-212 10 p.

Research output: Contribution to journalArticle

Corresponding angles
Spherical geometry
Dihedral angle
Euclidean geometry
Lobachevskian geometry
1 Citation (Scopus)

Computing and visualizing constant-curvature metrics on hyperbolic 3-manifolds with boundaries

Yin, X., Jin, M., Luo, F. & Gu, X. D., Dec 1 2008, Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings. PART 1 ed. p. 720-730 11 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 5358 LNCS, no. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hyperbolic 3-manifold
Manifolds with Boundary
Curvature
Metric
Computing