Uniqueness of subsolutions to the heat equation on Finsler measure spaces

Abstract

Let ( M, F, m ) be a forward complete Finsler measure space. In this paper, we prove that any nonnegative global subsolution in L p ( M )( p > 1) to the heat equation on R + × M is uniquely determined by the initial data. Moreover, we give an L p (0 < p ≤ 1) Liouville type theorem for nonnegative subsolutions u to the heat equation on R × M by establishing the local L p mean value inequality for u on M with Ric N ≥ − K ( K ≥ 0).