On the elliptic equation

on complete Riemannian manifolds

and their geometric applications

Authors:
Peter Li, Luen-fai Tam and DaGang Yang

Journal:
Trans. Amer. Math. Soc. **350** (1998), 1045-1078

MSC (1991):
Primary 58G03; Secondary 53C21

DOI:
https://doi.org/10.1090/S0002-9947-98-01886-8

MathSciNet review:
1407497

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the elliptic equation 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 and the hyperbolic space 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.

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Additional Information

**Peter Li**

Affiliation:
Department of Mathematics, University of California, Irvine, California 92697-3875

Email:
pli@math.uci.edu

**Luen-fai Tam**

Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Shatin, NT, Hong Kong

Email:
lftam@math.cuhk.edu.hk

**DaGang Yang**

Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118

Email:
dgy@math.tulane.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-01886-8

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

Received by editor(s):
May 23, 1995

Additional Notes:
The first two authors are partially supported by NSF grant DMS 9300422. The third author is partially supported by NSF grant DMS 9209330

Article copyright:
© Copyright 1998
American Mathematical Society