Integral Formulas for Differential Forms on Weighted Manifolds and Applications
Differential Geometry
2025-12-08 v1 Analysis of PDEs
Abstract
In this paper, we derive a Reilly formula for differential forms on weighted manifolds with nonempty boundary. As an application of this formula, we prove a Poincar\'e-type inequality in the same context and explore several of its consequences. We also present weighted versions of some boundary value problems and obtain new eigenvalue estimates that extend previously known results.
Cite
@article{arxiv.2512.05793,
title = {Integral Formulas for Differential Forms on Weighted Manifolds and Applications},
author = {Fida El Chami and Ola Makhoul},
journal= {arXiv preprint arXiv:2512.05793},
year = {2025}
}