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math.AP2026
Concavity and other properties of the entropy on manifolds
Xuenan Fu, Juanling Lu, Qi S. Zhang
In this paper, we establish systematic estimates for the entropy and its density on Riemannian manifolds, focusing on the more challenging cases where the Ricci curvature changes s…
math.AP2025
Backward Harnack inequality and Hamilton estimates for heat type equations
Juanling Lu, Yuting Wu, Qi S. Zhang
Based on gradient estimates for the heat equation by Hamilton, we discover a backward in time Harnack inequality for positive solutions on compact manifolds without further restric…