Weighted Poincaré inequality and the Poisson Equation
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- by Ovidiu Munteanu, Chiung-Jue Anna Sung and Jiaping Wang PDF
- Trans. Amer. Math. Soc. 374 (2021), 2167-2199 Request permission
Abstract:
We develop Green’s function estimates for manifolds satisfying a weighted Poincaré inequality together with a compatible lower bound on the Ricci curvature. This estimate is then applied to establish existence and sharp estimates of solutions to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete Kähler manifolds. Consequently, such Kähler manifolds must be connected at infinity.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
- Chiung-Jue Anna Sung
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsin-Chu, Taiwan
- MR Author ID: 357591
- Email: cjsung@math.nthu.edu.tw
- Jiaping Wang
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 262686
- Email: jiaping@math.umn.edu
- Received by editor(s): November 8, 2019
- Received by editor(s) in revised form: August 17, 2020
- Published electronically: December 18, 2020
- Additional Notes: Chiung-Jue Anna Sung is the corresponding author
The first author was partially supported by NSF grant DMS-1506220. The second author was partially supported by MOST
The third author was partially supported by NSF grant DMS-1606820. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 2167-2199
- MSC (2020): Primary 58J05, 53C55; Secondary 35J05
- DOI: https://doi.org/10.1090/tran/8291
- MathSciNet review: 4216736