Intertwining relations for diffusions in manifolds and applications to functional inequalities

TL;DR

This paper establishes intertwining relations for Markov semi-groups on manifolds, extending previous Euclidean results to Riemannian settings and non-symmetric operators, with applications to functional inequalities.

Contribution

It generalizes intertwining relations to Riemannian manifolds and non-symmetric operators, broadening their applicability in geometric analysis.

Findings

Derived new intertwining relations for Markov semi-groups on manifolds.

Applied these relations to establish Brascamp-Lieb type inequalities.

Extended spectral gap results to non-symmetric twisted operators.

Abstract

We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes the results of [1] from the Euclidean space to Riemannian manifolds and to non symmetric twisted operators.