Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

Zonglao Zhang; Zongben Xu

doi:10.1016/j.jmaa.2004.03.003

Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

Zonglao Zhang
, Zongben Xu

数学与统计学院

Xi'an Jiaotong University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

Let (M,g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function on M. We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.

源语言	英语
页（从-至）	655-665
页数	11
期刊	Journal of Mathematical Analysis and Applications
卷	294
期	2
DOI	https://doi.org/10.1016/j.jmaa.2004.03.003
出版状态	已出版 - 15 6月 2004

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title = "Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature",

abstract = "Let (M,g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function on M. We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.",

keywords = "Complete Riemannian manifold, Conformal deformation, Partial differential equation, Scalar curvature",

author = "Zonglao Zhang and Zongben Xu",

year = "2004",

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TY - JOUR

T1 - Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

AU - Zhang, Zonglao

AU - Xu, Zongben

PY - 2004/6/15

Y1 - 2004/6/15

N2 - Let (M,g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function on M. We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.

AB - Let (M,g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function on M. We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.

KW - Complete Riemannian manifold

KW - Conformal deformation

KW - Partial differential equation

KW - Scalar curvature

UR - https://www.scopus.com/pages/publications/3142662520

U2 - 10.1016/j.jmaa.2004.03.003

DO - 10.1016/j.jmaa.2004.03.003

M3 - 文章

AN - SCOPUS:3142662520

SN - 0022-247X

VL - 294

SP - 655

EP - 665

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

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