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A Poincaré Formula for Differential Forms and Applications
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Nicolas Ginoux and Georges Habib and Simon Raulot},
     title = {A {Poincar\'e} {Formula} for {Differential} {Forms} and {Applications}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2023},
     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a87/}
}
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Nicolas Ginoux; Georges Habib; Simon Raulot. A Poincaré Formula for Differential Forms and Applications. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a87/

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