The $a_{5}$ heat kernel coefficient on a manifold with boundary

TL;DR

This paper calculates the $a_{5}$ heat kernel coefficient for Laplace-type operators on compact manifolds with boundary, considering Dirichlet and Robin boundary conditions, advancing spectral geometry understanding.

Contribution

It provides the explicit computation of the $a_{5}$ coefficient for Laplace operators with boundary conditions, a previously uncalculated term in heat kernel expansion.

Findings

Explicit formula for $a_{5}$ coefficient derived

Results applicable to spectral geometry and quantum field theory

Enhances understanding of boundary effects in heat kernel expansion

Abstract

In this letter we present the calculation of the $a_{5}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with Dirichlet and Robin boundary conditions.