Heat kernel asymptotics with mixed boundary conditions

TL;DR

This paper computes the $a_5$ coefficient in the heat kernel asymptotic expansion for Laplace-type operators with mixed boundary conditions on compact manifolds, advancing understanding of spectral geometry.

Contribution

It provides the first explicit calculation of the $a_5$ coefficient for mixed boundary conditions on general compact manifolds.

Findings

Explicit formula for $a_5$ coefficient derived

Enhanced understanding of spectral invariants with mixed boundary conditions

Methodology applicable to other boundary value problems

Abstract

We calculate the coefficient $a_5$ of the heat kernel asymptotics for an operator of Laplace type with mixed boundary conditions on a general compact manifold.