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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Gradient estimate for harmonic functions on Kähler manifolds


Authors: Ovidiu Munteanu and Lihan Wang
Journal: Trans. Amer. Math. Soc. 372 (2019), 8759-8791
MSC (2010): Primary 53C21; Secondary 58J50
DOI: https://doi.org/10.1090/tran/7891
Published electronically: June 28, 2019
MathSciNet review: 4029711
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Abstract: We prove a sharp integral gradient estimate for harmonic functions on noncompact Kähler manifolds. As an application, we obtain a sharp estimate for the bottom of spectrum of the $ p$-Laplacian and prove a splitting theorem for manifolds achieving this estimate.


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Additional Information

Ovidiu Munteanu
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
Email: ovidiu.munteanu@uconn.edu

Lihan Wang
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
Email: lihan.wang@uconn.edu

DOI: https://doi.org/10.1090/tran/7891
Received by editor(s): December 24, 2018
Received by editor(s) in revised form: April 3, 2019
Published electronically: June 28, 2019
Additional Notes: The first author was partially supported by NSF grant DMS-811845.
Article copyright: © Copyright 2019 American Mathematical Society