Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remark on ``A problem of prescribing Gaussian curvature on $ S^2$" [Proc. Amer. Math. Soc. 129 (2001), no. 12, 3757-3758]


Author: Edward M. Fan
Journal: Proc. Amer. Math. Soc. 135 (2007), 107-108
MSC (2000): Primary 35J60; Secondary 31B30, 35J30, 53C21
Published electronically: June 13, 2006
MathSciNet review: 1860514
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we remark on a 2001 paper of S. Goyal and V. Goyal. The main result of this work is that they used some elementary method to find a class of functions $ K(x)=K(x_1,x_2,x_3)$ for which the solutions to

$\displaystyle \Delta u + K(x)e^{2u} = 1$

on $ S^2$ can be obtained. We observe that this class of functions that they studied is actually the trivial one, i.e. the class of positive constant functions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J60, 31B30, 35J30, 53C21

Retrieve articles in all journals with MSC (2000): 35J60, 31B30, 35J30, 53C21


Additional Information

Edward M. Fan
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: efan@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08461-9
PII: S 0002-9939(06)08461-9
Keywords: Laplace operator, Gaussian curvature
Received by editor(s): July 18, 2005
Published electronically: June 13, 2006
Additional Notes: This work was partially supported by NSF Graduate Research Fellowship
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society