Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



The best constant of the Moser-Trudinger inequality on $\textbf{S}^2$

Author: Yuji Sano
Journal: Trans. Amer. Math. Soc. 356 (2004), 3477-3482
MSC (2000): Primary 34A26; Secondary 53C55
Published electronically: November 25, 2003
MathSciNet review: 2055742
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the best constant of the Moser-Trudinger inequality on $\textbf{S}^2$ under a certain orthogonality condition. Applying Moser's calculation, we construct a counterexample to the sharper inequality with the condition.

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

  • 1. T. Aubin: Meilleures constantes dans le théor^ eme d'inclusion de Sobolev et un théor^ eme de Fredholm non linéaire pour la transformation conforme de la courbure scalaire. J. Funct. Anal. 32 (1979), no. 2, 148-174. MR 80i:58043
  • 2. T. Aubin: Some nonlinear problems in Riemannian geometry. Springer-Verlag, Berlin, 1998. MR 99i:58001
  • 3. W. Ding: Remarks on the existence problem of positive Kähler-Einstein metrics. Math. Ann. 282 (1988), no. 3, 463-471. MR 90a:58186
  • 4. A. Futaki and Y.Nakagawa: Characters of automorphism groups associated with Kähler classes and functionals with cocycle conditions. Kodai Math. J. 24 (2001), no. 1, 1-14. MR 2002c:32038
  • 5. J. Moser: A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J. 20 (1970/71), 1077-1092. MR 46:662
  • 6. J. Moser: On a nonlinear problem in differential geometry. Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971), pp. 273-280. Academic Press, New York, 1973. MR 49:4018
  • 7. G. Tian: Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130 (1997), no. 1, 1-37. MR 99e:53065

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 34A26, 53C55

Retrieve articles in all journals with MSC (2000): 34A26, 53C55

Additional Information

Yuji Sano
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

Keywords: The Moser-Trudinger inequality
Received by editor(s): March 12, 2003
Published electronically: November 25, 2003
Additional Notes: This research was partially supported by the Ministry of Education, Science, Sports and Culture of Japan, Grant-in-Aid for JSPS Fellows, 03340, 2003
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society