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arXiv · 2307.03616

A Poincar\'e formula for differential forms and applications

Nicolas Ginoux·Georges Habib·Simon Raulot
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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.

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Nicolas Ginoux, Georges Habib, Simon Raulot. 2023-07-07. A Poincar\'e formula for differential forms and applications. https://doi.org/10.3842/sigma.2023.088

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