ON THE ELLIPTIC EQUATION DELTA-U-KU(P)=0 ON COMPLETE RIEMANNIAN-MANIFOLDS AND THEIR GEOMETRIC APPLICATIONS(KU)

Authors
LI P TAM LF YANG DG
Citation
P. Li et al., ON THE ELLIPTIC EQUATION DELTA-U-KU(P)=0 ON COMPLETE RIEMANNIAN-MANIFOLDS AND THEIR GEOMETRIC APPLICATIONS(KU), Transactions of the American Mathematical Society, 350(3), 1998, pp. 1045-1078
Citations number
42
Categorie Soggetti
Mathematics,Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
350
Issue
3
Year of publication
1998
Pages
1045 - 1078
Database
ISI
SICI code
0002-9947(1998)350:3<1045:OTEEDO>2.0.ZU;2-E
Abstract
We study the elliptic equation Delta u + ku - Ku(p) = 0 on complete no ncompact Riemannian manifolds with K nonnegative. Three fundamental th eorems for this equation are proved in this paper. Complete analyses o f this equation on the Euclidean space R-n and the hyperbolic space 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.