September/October 2016 Prescribing integral curvature equation
Meijun Zhu
Differential Integral Equations 29(9/10): 889-904 (September/October 2016). DOI: 10.57262/die/1465912608

Abstract

In this paper we define new curvature functions on $\mathbb{S}^n$ via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even orders. Existence result for antipodally symmetric prescribed curvature functions on $\mathbb{S}^n$ is obtained. As a corollary, the existence of a conformal metric for an antipodally symmetric prescribed $Q-$curvature functions on $\mathbb{S}^3$ is proved. Curvature functions on general compact manifolds as well as the conformal covariance property for the corresponding integral operator are also addressed.

Citation

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Meijun Zhu. "Prescribing integral curvature equation." Differential Integral Equations 29 (9/10) 889 - 904, September/October 2016. https://doi.org/10.57262/die/1465912608

Information

Published: September/October 2016
First available in Project Euclid: 14 June 2016

zbMATH: 06644053
MathSciNet: MR3513585
Digital Object Identifier: 10.57262/die/1465912608

Subjects:
Primary: 35J60 , 58J05

Rights: Copyright © 2016 Khayyam Publishing, Inc.

Vol.29 • No. 9/10 • September/October 2016
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