Gradient estimate for harmonic functions on Kähler manifolds
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- by Ovidiu Munteanu and Lihan Wang PDF
- Trans. Amer. Math. Soc. 372 (2019), 8759-8791 Request permission
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.References
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Additional Information
- Ovidiu Munteanu
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
- MR Author ID: 698338
- Email: ovidiu.munteanu@uconn.edu
- Lihan Wang
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
- MR Author ID: 1036689
- Email: lihan.wang@uconn.edu
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 8759-8791
- MSC (2010): Primary 53C21; Secondary 58J50
- DOI: https://doi.org/10.1090/tran/7891
- MathSciNet review: 4029711