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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 088, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.088 (Mi sigma1983) 		 
A Poincaré Formula for Differential Forms and Applications

Nicolas Ginouxa, Georges Habibba, Simon Raulotc

a Université de Lorraine, CNRS, IECL, F-57000 Metz, France
b Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn, Lebanon
c Université de Rouen Normandie, CNRS, Normandie Univ, LMRS UMR 6085, F-76000 Rouen, France
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DOI: https://doi.org/10.3842/SIGMA.2023.088
Abstract: We prove a new general Poincaré-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.
Keywords: manifolds with boundary, boundary value problems, Hodge Laplace operator, rigidity results.
Received: July 19, 2023; in final form October 26, 2023; Published online November 8, 2023
Document Type: Article
MSC: 53C21, 53C24, 58J32, 58J50
Language: English
Citation: Nicolas Ginoux, Georges Habib, Simon Raulot, “A Poincaré Formula for Differential Forms and Applications”, SIGMA, 19 (2023), 088, 17 pp.
Citation in format AMSBIB
\Bibitem{GinHabRau23}
\by Nicolas~Ginoux, Georges~Habib, Simon~Raulot
\paper A Poincar\'e Formula for Differential Forms and Applications
\jour SIGMA
\yr 2023
\vol 19
\papernumber 088
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma1983}
\crossref{https://doi.org/10.3842/SIGMA.2023.088}
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