Transactions of the American Mathematical Society

On the elliptic equation $\Delta u + ku - Ku^{p} = 0$ on complete Riemannian manifolds and their geometric applications

Author(s): Peter Li; Luen-fai Tam; DaGang Yang
Journal: Trans. Amer. Math. Soc. 350 (1998), 1045-1078.
MSC (1991): Primary 58G03; Secondary 53C21
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Abstract: We study the elliptic equation $\Delta u + ku - Ku^{p} = 0$ on complete noncompact Riemannian manifolds with $K$

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 $k$

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 58G03, 53C21

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: 10.1090/S0002-9947-98-01886-8
PII: S 0002-9947(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
Copyright of article: Copyright 1998, American Mathematical Society

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