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arXiv · 1904.13337

Weighted Poincare inequality and the Poisson equation

Ovidiu Munteanu·Chiung-Jue Anna Sung·Jiaping Wang
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Abstract

We develop Green's function estimate for manifolds satisfying a weighted Poincare inequality together with a compatible lower bound on the Ricci curvature. The estimate is then applied to establish existence and sharp estimates of the solution 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.

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Ovidiu Munteanu, Chiung-Jue Anna Sung, Jiaping Wang. 2019-04-30. Weighted Poincare inequality and the Poisson equation. https://arxiv.org/abs/1904.13337

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