Some integral inequalities on weighted Riemannian manifolds with boundary

TL;DR

This paper explores integral inequalities on weighted Riemannian manifolds with boundary, extending Reilly's formula for the $\,\phi$-Laplacian to derive Brascamp-Lieb and Colesanti type inequalities.

Contribution

It introduces new integral inequalities on weighted Riemannian manifolds with boundary using a generalized Reilly formula for the $\,\phi$-Laplacian, expanding existing mathematical frameworks.

Findings

Derived new Brascamp-Lieb type inequalities

Established Colesanti type inequalities

Extended Reilly's integral formula to weighted manifolds

Abstract

In this paper, we continue to study some applications with respect to a Reilly type integral formula associated with the $\phi$-Laplacian. Some inequalities of Brascamp-Lieb type and Colesanti type are provided.