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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the elliptic equation $\Delta u+ku-Ku^p=0$ on complete Riemannian manifolds and their geometric applications
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by Peter Li, Luen-fai Tam and DaGang Yang PDF
Trans. Amer. Math. Soc. 350 (1998), 1045-1078 Request permission

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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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
  • MR Author ID: 170445
  • Email: lftam@math.cuhk.edu.hk
  • DaGang Yang
  • Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
  • Email: dgy@math.tulane.edu
  • 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 1998 American Mathematical Society
  • 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