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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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On the gradient estimate of Cheng and Yau
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by Ovidiu Munteanu PDF
Proc. Amer. Math. Soc. 140 (2012), 1437-1443 Request permission

Abstract:

We improve the well-known local gradient estimate of Cheng and Yau in the case when the Ricci curvature has a negative lower bound.
References
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  • Peter Wai-Kwong Li, Harmonic functions and applications to complete manifolds, XIV Escola de Geometria Diferencial. [XIV School of Differential Geometry], Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2006. MR 2369440
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  • Xiaodong Wang, Harmonic functions, entropy, and a characterization of the hyperbolic space, J. Geom. Anal. 18 (2008), no. 1, 272–284. MR 2365675, DOI 10.1007/s12220-007-9001-z
  • Shing Tung Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228. MR 431040, DOI 10.1002/cpa.3160280203
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Additional Information
  • Ovidiu Munteanu
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • MR Author ID: 698338
  • Email: omuntean@math.columbia.edu
  • Received by editor(s): December 28, 2010
  • Published electronically: September 1, 2011
  • Additional Notes: The author’s research was partially supported by NSF grant No. DMS-1005484
  • Communicated by: Michael Wolf
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1437-1443
  • MSC (2010): Primary 53C21; Secondary 58J05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11304-2
  • MathSciNet review: 2869128