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
- 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
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