Georges Habib (Lebanese University, Beirut)
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 the limiting case. Also a new Ros-type inequality for differential forms is derived assuming the existence of a nonzero parallel form on the manifold. This work is joint with Nicolas Ginoux and Simon Raulot.
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