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

220 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.",

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AU - Gursky, Matthew J.

AU - Yang, Paul C.

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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

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DO - 10.1007/BF01191617

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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ER -

The scalar curvature equation on 2- and 3-spheres

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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