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Pré-Publication, Document De Travail Année : 2022

First boundary Dirac eigenvalue and boundary capacity potential

Résumé

We derive new lower bounds for the first eigenvalue of the Dirac operator of an oriented hypersurface Σ bounding a noncompact domain in a spin asymptotically flat manifold (M n , g) with nonnegative scalar curvature. These bounds involve the boundary capacity potential and, in some cases, the capacity of Σ in (M n , g) yielding several new geometric inequalities. The proof of our main result relies on an estimate for the first eigenvalue of the Dirac operator of boundaries of compact Riemannian spin manifolds endowed with a singular metric which may have independent interest.
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Dates et versions

hal-03703550 , version 1 (24-06-2022)

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  • HAL Id : hal-03703550 , version 1

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Simon Raulot. First boundary Dirac eigenvalue and boundary capacity potential. 2022. ⟨hal-03703550⟩
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