Heat kernels on curved cones

TL;DR

This paper derives a formula for the heat kernel expansion on curved cones with singularities, highlighting the role of extrinsic curvature in the expansion.

Contribution

It provides a functorial derivation of the heat kernel coefficient on manifolds with codimension-two singular fixed points, emphasizing extrinsic curvature effects.

Findings

Derived heat kernel expansion coefficient for curved cones.

Identified the presence of extrinsic curvature terms.

Established a functorial approach to the derivation.

Abstract

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.