The scalar curvature equation on 2- and 3-spheres

Sun Yung A. Chang; Matthew J. Gursky; Paul C. Yang

doi:10.1007/BF01191617

The scalar curvature equation on 2- and 3-spheres

Sun Yung A. Chang, Matthew J. Gursky, Paul C. Yang

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

224 Scopus citations

Abstract

In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.

Original language	English (US)
Pages (from-to)	205-229
Number of pages	25
Journal	Calculus of Variations and Partial Differential Equations
Volume	1
Issue number	2
DOIs	https://doi.org/10.1007/BF01191617
State	Published - May 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Mathematics subject classifications: 35J60, 58G03

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10.1007/BF01191617

Cite this

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title = "The scalar curvature equation on 2- and 3-spheres",

abstract = "In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.",

keywords = "Mathematics subject classifications: 35J60, 58G03",

author = "Chang, \{Sun Yung A.\} and Gursky, \{Matthew J.\} and Yang, \{Paul C.\}",

year = "1993",

month = may,

doi = "10.1007/BF01191617",

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journal = "Calculus of Variations and Partial Differential Equations",

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T1 - The scalar curvature equation on 2- and 3-spheres

AU - Chang, Sun Yung A.

AU - Gursky, Matthew J.

AU - Yang, Paul C.

PY - 1993/5

Y1 - 1993/5

N2 - In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.

AB - In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.

KW - Mathematics subject classifications: 35J60, 58G03

UR - https://www.scopus.com/pages/publications/34250074537

UR - https://www.scopus.com/inward/citedby.url?scp=34250074537&partnerID=8YFLogxK

U2 - 10.1007/BF01191617

DO - 10.1007/BF01191617

M3 - Article

AN - SCOPUS:34250074537

SN - 0944-2669

VL - 1

SP - 205

EP - 229

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 2

ER -

The scalar curvature equation on 2- and 3-spheres

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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