%AMunteanu, Ovidiu%ASung, Chiung-Jue%AWang, Jiaping%BJournal Name: Transactions of the American Mathematical Society; Journal Volume: 374; Journal Issue: 1042
%D2021%I
%JJournal Name: Transactions of the American Mathematical Society; Journal Volume: 374; Journal Issue: 1042
%K
%MOSTI ID: 10430931
%PMedium: X
%TWeighted Poincaré inequality and the Poisson Equation
%XWe 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.
%0Journal Article