Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces

Zhenan Sui

doi:10.1007/s12220-016-9703-1

Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces

Zhenan Sui^*

^*Corresponding author for this work

Ohio State University

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

11 Scopus citations

Abstract

We show the existence and nonexistence results of complete conformal metrics with prescribed symmetric functions of the eigenvalues of the Ricci tensor defined on negative cones on Euclidean spaces. Our results are sharp under certain decay conditions of the prescribed curvature functions.

Original language	English
Pages (from-to)	893-907
Number of pages	15
Journal	Journal of Geometric Analysis
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s12220-016-9703-1
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

Complete conformal metrics
Ricci curvature
Subsolution
Supersolution

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10.1007/s12220-016-9703-1

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title = "Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces",

abstract = "We show the existence and nonexistence results of complete conformal metrics with prescribed symmetric functions of the eigenvalues of the Ricci tensor defined on negative cones on Euclidean spaces. Our results are sharp under certain decay conditions of the prescribed curvature functions.",

keywords = "Complete conformal metrics, Ricci curvature, Subsolution, Supersolution",

author = "Zhenan Sui",

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AB - We show the existence and nonexistence results of complete conformal metrics with prescribed symmetric functions of the eigenvalues of the Ricci tensor defined on negative cones on Euclidean spaces. Our results are sharp under certain decay conditions of the prescribed curvature functions.

KW - Complete conformal metrics

KW - Ricci curvature

KW - Subsolution

KW - Supersolution

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Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces

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Keywords

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