On the elliptic equation <IMG ALIGN=MIDDLE > on complete Riemannian manifolds and their geometric applications期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the elliptic equation on complete Riemannian manifolds and their geometric applications

Authors:	Peter Li Luen-fai Tam DaGang Yang

Affiliation:	Department of Mathematics, University of California, Irvine, California 92697-3875 ; Department of Mathematics, Chinese University of Hong Kong, Shatin, NT, Hong Kong ; Department of Mathematics, Tulane University, New Orleans, Louisiana 70118

Abstract:	We study the elliptic equation $Delta u + ku - Ku^{p} = 0$ on complete noncompact Riemannian manifolds with nonnegative. Three fundamental theorems for this equation are proved in this paper. Complete analyses of this equation on the Euclidean space ${mathbf{R}}^{n}$ and the hyperbolic space ${mathbf{H}}^{n}$ are carried out when is a constant. Its application to the problem of conformal deformation of nonpositive scalar curvature will be done in the second part of this paper.

Keywords:	Conformal deformation prescribing scalar curvature complete Riemannian manifolds semi-linear elliptic PDE generalized maximum principle analysis on manifolds

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