On Witten Laplacians and Brascamp–Lieb’s Inequality on Manifolds with Boundary

In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp–Lieb’s type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms...

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Veröffentlicht in:	Integral equations and operator theory 2017-03, Vol.87 (3), p.411-434
1. Verfasser:	Le Peutrec, Dorian
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Analysis of PDEs Differential Geometry Dirichlet problem Functional Analysis Inequalities Mathematics Mathematics and Statistics Quadratic forms Riemann manifold Spectral Theory Supersymmetry Theorems Topological manifolds
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creator	Le Peutrec, Dorian
description	In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp–Lieb’s type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms associated with the Neumann and Dirichlet self-adjoint realizations of the Witten Laplacian. They moreover imply the usual Brascamp–Lieb’s inequality and its generalization to compact Riemannian manifolds without boundary.
doi_str_mv	10.1007/s00020-017-2354-1
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subjects	Analysis Analysis of PDEs Differential Geometry Dirichlet problem Functional Analysis Inequalities Mathematics Mathematics and Statistics Quadratic forms Riemann manifold Spectral Theory Supersymmetry Theorems Topological manifolds
title	On Witten Laplacians and Brascamp–Lieb’s Inequality on Manifolds with Boundary
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