A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound

Yan Yan Li; Luc Nguyen

doi:10.1016/j.jfa.2013.08.004

A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound

Yan Yan Li, Luc Nguyen

School of Arts and Sciences, Mathematics

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

5 Scopus citations

Abstract

We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions when the associated cone Γ; satisfies μΓ;+≤1, which includes the σ_k-Yamabe problem for k not smaller than half of the dimension of the manifold.

Original language	English (US)
Pages (from-to)	3741-3771
Number of pages	31
Journal	Journal of Functional Analysis
Volume	266
Issue number	6
DOIs	https://doi.org/10.1016/j.jfa.2013.08.004
State	Published - Mar 15 2014

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Compactness and existence of solutions
Fully nonlinear Yamabe problem

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10.1016/j.jfa.2013.08.004

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abstract = "We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions when the associated cone Γ; satisfies μΓ;+≤1, which includes the σk-Yamabe problem for k not smaller than half of the dimension of the manifold.",

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AU - Nguyen, Luc

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KW - Fully nonlinear Yamabe problem

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