New eigenvalue estimates involving Bessel functions
El Chami, Fida (Lebanese University)
Habib, Georges (Lebanese University)
Ginoux, Nicolas (Universit'e de Lorraine)

Date:	2021
Abstract:	Given a compact Riemannian manifold (Mn, g) with boundary ∂M, we give an estimate for the quotient R ∂M f dµg R M f dµg , where f is a smooth positive function defined on M that satisfies some inequality involving the scalar Laplacian. By the mean value lemma established in [39], we provide a differential inequality for f which, under some curvature assumptions, can be interpreted in terms of Bessel functions. As an application of our main result, a new inequality is given for Dirichlet and Robin Laplacian. Also, a new estimate is established for the eigenvalues of the Dirac operator that involves a positive root of Bessel function besides the scalar curvature. Indepen[1]dently, we extend the Robin Laplacian on functions to differential forms. We prove that this natural extension defines a self-adjoint and elliptic operator whose spectrum is discrete and consists of positive real eigenvalues. In particular, we characterize its first eigenvalue and provide a lower bound of it in terms of Bessel functions.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Bessel functions ; Eigenvalues ; Dirac operator ; Yamabe operator ; Robin laplacian
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 2 (2021) , p. 681-726 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/390245
DOI: 10.5565/PUBLMAT6522109

46 p, 529.9 KB

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