Heat Kernel Expansion for Semitransparent Boundaries

TL;DR

This paper investigates the heat kernel asymptotics for Laplace-type operators with delta-function potentials on surfaces, deriving general formulas and calculating initial coefficients to understand boundary effects.

Contribution

It provides explicit formulas for heat kernel coefficients in the presence of semitransparent boundaries with delta potentials, advancing boundary condition analysis.

Findings

Derived general small t asymptotics for the heat kernel.

Explicit calculation of initial heat kernel coefficients.

Enhanced understanding of boundary effects in Laplace operators.

Abstract

We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel coefficients.