Heat Content, Heat Trace, and Isospectrality

TL;DR

This paper investigates the relationships between heat content, heat trace, and isospectrality for Laplacians on compact manifolds, focusing on finite coverings and warped products to understand spectral properties.

Contribution

It introduces new insights into how heat invariants relate to isospectrality in the context of finite coverings and warped product manifolds.

Findings

Heat content and heat trace are analyzed in relation to isospectrality.

Finite coverings influence spectral properties and heat invariants.

Warped products provide a framework for understanding spectral geometry.

Abstract

We study the heat content function, the heat trace function, and questions of isospectrality for the Laplacian with Dirichlet boundary conditions on a compact manifold with smooth boundary in the context of finite coverings and warped products.