• 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
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Article
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
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
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
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
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

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
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
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
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
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

Computing constant-curvature metrics for hyperbolic 3-manifolds with boundaries using truncated tetrahedral meshes

Yin, X., Jin, M., Luo, F. & Gu, X. D., Dec 1 2008, In : International Journal of Shape Modeling. 14, 2, p. 169-188 20 p.

Research output: Contribution to journalArticle

Tetrahedral Mesh
Hyperbolic 3-manifold
Manifolds with Boundary
Curvature
Metric
167 Citations (Scopus)

Discrete surface Ricci flow

Jin, M., Kim, J., Luo, F. & Gu, X., Sep 1 2008, In : IEEE Transactions on Visualization and Computer Graphics. 14, 5, p. 1030-1043 14 p., 4483509.

Research output: Contribution to journalArticle

Medical imaging
Newton-Raphson method
Parameterization
Topology
Hot Temperature
6 Citations (Scopus)

Geodesic ideal triangulations exist virtually

Luo, F., Schleimer, S. & Tillmann, S., Jul 1 2008, In : Proceedings of the American Mathematical Society. 136, 7, p. 2625-2630 6 p.

Research output: Contribution to journalArticle

Hyperbolic Manifold
Triangulation
Finite Volume
Geodesic
Cover
14 Citations (Scopus)

Manifold splines with a single extraordinary point

Gu, X., He, Y., Jin, M., Luo, F., Qin, H. & Yau, S. T., Jun 1 2008, In : CAD Computer Aided Design. 40, 6, p. 676-690 15 p.

Research output: Contribution to journalArticle

Splines
Topology
Pipelines
39 Citations (Scopus)

Optimal surface parameterization using inverse curvature map

Yang, Y. L., Kim, J., Luo, F., Hu, S. M. & Gu, X., Sep 1 2008, In : IEEE Transactions on Visualization and Computer Graphics. 14, 5, p. 1054-1066 13 p., 4479457.

Research output: Contribution to journalArticle

Parameterization
Conformal mapping
Poisson equation
Computer graphics
2007
13 Citations (Scopus)

Computing general geometric structures on surfaces using Ricci flow

Jin, M., Luo, F. & Gu, X. D., Aug 1 2007, In : CAD Computer Aided Design. 39, 8, p. 663-675 13 p.

Research output: Contribution to journalArticle

Geometry
Splines
Computer aided design
13 Citations (Scopus)

On teichmüller spaces of surfaces with boundary

Luo, F., Sep 15 2007, In : Duke Mathematical Journal. 139, 3, p. 463-482 20 p.

Research output: Contribution to journalArticle

Hyperbolic Metric
Parameterization
Convex Polytope
Symplectic Form
Cusp
6 Citations (Scopus)

Volume and angle structures on 3-manifolds

Luo, F., Dec 2007, In : Asian Journal of Mathematics. 11, 4, p. 555-566 12 p.

Research output: Contribution to journalArticle

Triangulation
Angle
Moduli Space
Closed
Triangular pyramid
2006
6 Citations (Scopus)

A characterization of spherical polyhedral surfaces

Luo, F., Jan 1 2006, In : Journal of Differential Geometry. 74, 3, p. 407-424 18 p.

Research output: Contribution to journalArticle

Spherical triangle
Angle
Convex Polytope
Gluing
Isometric
6 Citations (Scopus)

Continuity of the volume of simplices in classical geometry

Luo, F., Jun 1 2006, In : Communications in Contemporary Mathematics. 8, 3, p. 411-431 21 p.

Research output: Contribution to journalArticle

Dihedral angle
Geometry
Minor
Verify
2005
10 Citations (Scopus)
Curvature Flow
Manifolds with Boundary
Hyperbolic Metric
Totally Geodesic
Triangulation
2004
87 Citations (Scopus)

Combinatorial Yamabe flow on surfaces

Luo, F., Oct 1 2004, In : Communications in Contemporary Mathematics. 6, 5, p. 765-780 16 p.

Research output: Contribution to journalArticle

Triangulation
Surgery
Metric
Curvature
Geometry
2 Citations (Scopus)

Dehn-Thurston coordinates for curves on surfaces

Luo, F. & Stong, R., Jan 1 2004, In : Communications in Analysis and Geometry. 12, 1-2, p. 1-41 41 p.

Research output: Contribution to journalArticle

Intersection number
Lamination
Cauchy
Curve