A Poincar\'e formula for differential forms and applications
Differential Geometry
2023-11-09 v2 Analysis of PDEs
Abstract
We prove a new general Poincar\'e-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived assuming the existence of a nonzero parallel form on the manifold.
Cite
@article{arxiv.2307.03616,
title = {A Poincar\'e formula for differential forms and applications},
author = {Nicolas Ginoux and Georges Habib and Simon Raulot},
journal= {arXiv preprint arXiv:2307.03616},
year = {2023}
}