Yet another heat semigroup characterization of BV functions on Riemannian manifolds

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Heat Invariants of Riemannian Manifolds

We obtain explicit formulas for the local heat invariants of arbitrary Riemannian manifolds without boundary. Our approach is based on a multi-dimensional generalization of the Agmon-Kannai method.

BV functions and sets of finite perimeter in sub-Riemannian manifolds

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms Gp : TpM → [0,∞] are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets ...

Geometric Heat Comparison Criteria for Riemannian Manifolds

The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustr...

Differential Harnack Inequalities on Riemannian Manifolds I : Linear Heat Equation

Abstract. In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with Ricci(M) ≥ −k, k ∈ R. As applications, several parabolic Harnack inequalities are obtained and they lead to new estimates on heat kernels of manifolds with Ricci curvature bounded from below. In the second part, we establish a Perelman type L...