Heat Content Asymptotics for Riemannian manifolds with Zaremba boundary conditions

TL;DR

This paper establishes the existence of a full asymptotic expansion for heat content on Riemannian manifolds with Zaremba boundary conditions and computes the first three coefficients using geometric invariants.

Contribution

It proves the existence of the heat content asymptotic expansion for Zaremba boundary conditions and explicitly determines the first three coefficients.

Findings

Full asymptotic expansion exists for heat content with Zaremba conditions

First three coefficients are explicitly computed in terms of geometric invariants

Partial information obtained about the fourth coefficient

Abstract

The existence of a full asymptotic expansion for the heat content asymptotics of an operator of Laplace type with classical Zaremba boundary conditions on a smooth manifold is established. The first three coefficients in this asymptotic expansion are determined in terms of geometric invariants; partial information is obtained about the fourth coefficient.