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

Research output: Contribution to journal › Article › peer-review

37 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 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

Access to Document

10.1090/S0002-9947-1993-1087058-5

Cite this

@article{3a63d1d5730b4bb58517708d19c894d4,

title = "Remarks on prescribing gauss curvature",

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.",

author = "Xingwang Xu and Yang, \{Paul C.\}",

year = "1993",

month = apr,

doi = "10.1090/S0002-9947-1993-1087058-5",

language = "English (US)",

volume = "336",

pages = "831--840",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Remarks on prescribing gauss curvature

AU - Xu, Xingwang

AU - Yang, Paul C.

PY - 1993/4

Y1 - 1993/4

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/0041151805

UR - https://www.scopus.com/inward/citedby.url?scp=0041151805&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1993-1087058-5

DO - 10.1090/S0002-9947-1993-1087058-5

M3 - Article

AN - SCOPUS:0041151805

SN - 0002-9947

VL - 336

SP - 831

EP - 840

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

Remarks on prescribing gauss curvature

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this