Geometric Fokker-Planck equations.
Geometric heat kernel coefficient for APS-type boundary conditions
I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.
Gradient estimates, Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields.
Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds for the following general heat equation where is a constant and is a differentiable function defined on . We suppose that the Bakry-Émery curvature and the -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.
Group method analysis of two-dimensional plate in heat flux.