Remarks on prescribing gauss curvature

Xingwang Xu; Paul C. Yang

doi:10.1090/S0002-9947-1993-1087058-5

Remarks on prescribing gauss curvature

Xingwang Xu, Paul C. Yang

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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 language	English (US)
Pages (from-to)	831-840
Number of pages	10
Journal	Transactions of the American Mathematical Society
Volume	336
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1993-1087058-5
State	Published - Apr 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1993-1087058-5

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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.",

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AB - 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.

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Remarks on prescribing gauss curvature

Abstract

All Science Journal Classification (ASJC) codes

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