On the local solvability of the nirenberg problem on S2

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Abstract

We present some results on the local solvability of the Nirenberg problem on S2. More precisely, an L2(S2) function near 1 is the Gauss curvature of an H2(S2) metric on the round sphere S2, pointwise conformal to the standard round metric on S 2, provided its L2(S2) projection into the the space of spherical harmonics of degree 2 satisfy a matrix invertibility condition, and the ratio of the L2(S2) norms of its L 2(S2) projections into the the space of spherical harmonics of degree 1 vs the space of spherical harmonics of degrees other than 1 is sufficiently small.

Original languageEnglish (US)
Pages (from-to)607-615
Number of pages9
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number2
DOIs
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Local solvability
  • Nirenberg problem
  • Prescribing Gaussian curvature

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