Differential and Integral Equations

Prescribing integral curvature equation

Meijun Zhu

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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.

Article information

Source
Differential Integral Equations Volume 29, Number 9/10 (2016), 889-904.

Dates
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1465912608

Mathematical Reviews number (MathSciNet)
MR3513585

Zentralblatt MATH identifier
06644053

Subjects
Primary: 35J60: Nonlinear elliptic equations 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]

Citation

Zhu, Meijun. Prescribing integral curvature equation. Differential Integral Equations 29 (2016), no. 9/10, 889--904. https://projecteuclid.org/euclid.die/1465912608.


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