Local heat kernel

The paper is devoted to a local heat kernel, which is a special component of the standard heat kernel. Localization means that all considerations are performed in an open convex subset of a smooth Riemannian manifold. We discuss such properties and concepts as uniqueness, a symmetry of the Seeley–DeWitt coefficients, extension to the entire manifold, a family of special functions, and the late-time asymptotic behavior using the path integral approach.