Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Gaussian curvature in the negative case
HTML articles powered by AMS MathViewer

by Wenxiong Chen and Congming Li PDF
Proc. Amer. Math. Soc. 131 (2003), 741-744 Request permission

Abstract:

In this paper, we reinvestigate an old problem of prescribing Gaussian curvature in the negative case. In 1974, Kazdan and Warner considered the equation \[ - \bigtriangleup u + \alpha = R(x)e^u, \;\; x \in M, \] on any compact two dimensional manifold $M$ with $\alpha < 0$. They showed that there exists a number $\alpha _o$, such that the equation is solvable for every $0 > \alpha > \alpha _o$ and it is not solvable for $\alpha < \alpha _o$. Then one may naturally ask: Is the equation solvable for $\alpha = \alpha _o$? In this paper, we answer the question affirmatively. We show that there exists at least one solution for $\alpha = \alpha _o$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J60
  • Retrieve articles in all journals with MSC (2000): 35J60
Additional Information
  • Wenxiong Chen
  • Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
  • MR Author ID: 205322
  • Email: wec344f@smsu.edu
  • Congming Li
  • Affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80039
  • MR Author ID: 259914
  • Email: cli@newton.colorado.edu
  • Received by editor(s): October 12, 2000
  • Published electronically: October 15, 2002
  • Additional Notes: The first author was partially supported by NSF Grant DMS-0072328
    The second author was partially supported by NSF Grant DMS-9970530
  • Communicated by: Bennett Chow
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 741-744
  • MSC (2000): Primary 35J60
  • DOI: https://doi.org/10.1090/S0002-9939-02-06802-8
  • MathSciNet review: 1937411