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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


We improve the well-known local gradient estimate of Cheng and Yau in the case when the Ricci curvature has a negative lower bound.
  • E. Calabi, An extension of E. Hopf’s maximum principle with an application to Riemannian geometry, Duke Math. J. 25 (1958), 45–56. MR 92069
  • S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333–354. MR 385749, DOI 10.1002/cpa.3160280303
  • 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
  • Peter Li and Jiaping Wang, Complete manifolds with positive spectrum. II, J. Differential Geom. 62 (2002), no. 1, 143–162. MR 1987380
  • R. Schoen and S.-T. Yau, Lectures on differential geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I, International Press, Cambridge, MA, 1994. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang [Gong Qing Zhang], Jia Qing Zhong and Yi Chao Xu; Translated from the Chinese by Ding and S. Y. Cheng; With a preface translated from the Chinese by Kaising Tso. MR 1333601
  • 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:
  • 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:
  • MathSciNet review: 2869128