Remarks on prescribing gauss curvature

Xingwang Xu, Paul C. Yang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We study the nonlinear partial differential equation for the problem of prescribing Gauss curvature K on S2. We give an example of a rotationally symmetric K for which the Kazdan-Warner obstruction is satisfied but the equation has no rotationally symmetric solution. On the other hand, we give a simple sufficient condition for solvability of the equation when k is rotationally symmetric. Finally we give a sufficient condition for solvability when K is not necessarily rotationally symmetric.

Original languageEnglish (US)
Pages (from-to)831-840
Number of pages10
JournalTransactions of the American Mathematical Society
Volume336
Issue number2
DOIs
StatePublished - Apr 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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