A Grushin problem for Bismut's hypoelliptic Laplacian

TL;DR

This paper analyzes Bismut's hypoelliptic Laplacian's asymptotic behavior in high friction and low temperature limits, providing insights into its spectral properties and related geometric structures.

Contribution

It introduces a combined asymptotic framework for Bismut's hypoelliptic Laplacian in multiple regimes, advancing understanding of its spectral and geometric aspects.

Findings

Asymptotic descriptions in high friction regime

Behavior in low temperature limit

Connections to geometric structures

Abstract

We study in this article the combined asymptotic analysis of Bismut's hypoelliptic Laplacian, in the high friction b $\rightarrow$ 0+ and possibly low temperature h $\rightarrow$ 0+ regimes.