Spectral invariants of the Dirichlet-to-Neumann map associated to the Witten-Laplacian with potential

TL;DR

This paper develops a method to compute spectral invariants of the Dirichlet-to-Neumann map for the Witten-Laplacian with potential on compact Riemannian manifolds, revealing geometric and potential-related information.

Contribution

It provides an explicit procedure to calculate all spectral asymptotic coefficients and explicitly determines the first four, linking them to geometric and potential features.

Findings

Computed the full symbol of the Dirichlet-to-Neumann map.

Explicitly derived the first four spectral invariants.

Linked spectral invariants to geometric and potential data.

Abstract

For a compact connected Riemannian manifold with smooth boundary, we establish an effective procedure, by which we can calculate all the coefficients of the spectral asymptotic formula of the Dirichlet-to-Neumann map associated to the Witten-Laplacian with potential. In particular, by computing the full symbol of the Dirichlet-to-Neumann map we explicitly give the first four coefficients. They are spectral invariants, which provide precise information concerning the volume, curvatures, drifting function and potential.