The $a_{3/2}$ heat kernel coefficient for oblique boundary conditions

TL;DR

This paper introduces a method to compute the $a_{3/2}$ heat kernel coefficient for Laplace-type operators on manifolds with oblique boundary conditions, combining special case analysis and conformal transformations.

Contribution

It provides a novel approach to determine the $a_{3/2}$ heat kernel coefficient for oblique boundary conditions using a combination of special case evaluations and conformal techniques.

Findings

Derived the complete form of the $a_{3/2}$ heat kernel coefficient.

Established restrictions on coefficient forms through special case evaluations.

Applied conformal transformations to determine the smeared coefficient.

Abstract

We present a method for the calculation of the $a_{3/2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire smeared coefficient to be determined.