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On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds


Authors: Fabrice Baudoin, Maria Gordina and Phanuel Mariano
Journal: Proc. Amer. Math. Soc. 147 (2019), 3181-3189
MSC (2010): Primary 58J35; Secondary 53C17, 35H10
DOI: https://doi.org/10.1090/proc/14451
Published electronically: March 26, 2019
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Abstract: In this note we show how results in earlier works yield the Cheng-Yau estimate on two classes of sub-Riemannian manifolds: Carnot groups and sub-Riemannian manifolds satisfying a generalized curvature-dimension inequality.


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Additional Information

Fabrice Baudoin
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: fabrice.baudoin@uconn.edu

Maria Gordina
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: maria.gordina@uconn.edu

Phanuel Mariano
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: pmariano@purdue.edu

DOI: https://doi.org/10.1090/proc/14451
Keywords: Cheng-Yau estimate, Carnot groups, sub-Riemannian manifolds, curvature-dimension inequality
Received by editor(s): September 19, 2018
Received by editor(s) in revised form: October 18, 2018
Published electronically: March 26, 2019
Additional Notes: The research of the first author was supported in part by NSF Grant DMS-1660031.
The research of the second author was supported in part by the Simons Fellowship and NSF Grants DMS-1405169, DMS-1712427
The research of the third author was supported in part by NSF Grants DMS-1405169, DMS-1712427
Communicated by: Guofang Wei
Article copyright: © Copyright 2019 American Mathematical Society