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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

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A best constant and the Gaussian curvature
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by Chong Wei Hong PDF
Proc. Amer. Math. Soc. 97 (1986), 737-747 Request permission

Abstract:

For axisymmetric $f \in {C^\infty }({S^2})$ we find conditions to make $f$ the scalar curvature of a metric pointwise conformal to the standard metric of ${S^2}$. Closely related to these results, we prove that in the inequality (Moser [8]) \[ \int _{{S^2}} {{e^u} \leq C{e^{\left \| {\nabla u} \right \|_2^2/16\pi \quad }}\forall u \in H_1^2({S^2})} {\text { with }}\int _{{S^2}} {u = 0} ,\], the best constant $C = {\text {Vol(}}{{\text {S}}^2}{\text {)}}$.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 737-747
  • MSC: Primary 58G30; Secondary 35B45, 53C20, 58E99
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845999-7
  • MathSciNet review: 845999