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Reilly-Type Inequalities for Paneitz and Steklov Eigenvalues

  • Julien RothEmail author
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Abstract

We prove Reilly-type upper bounds for different types of eigenvalue problems on submanifolds of Euclidean spaces with density. This includes the eigenvalues of Paneitz-like operators as well as three types of generalized Steklov problems. In the case without density, the equality cases are discussed and we prove some stability results for hypersurfaces which derive from a general pinching result about the moment of inertia.

Keywords

Paneitz operator Steklov problem Eigenvalues Hypersurfaces Pinching 

Mathematics Subject Classification (2010)

35P15 53C20 53C24 53C42 58C40 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques AppliquéesUPEM-UPEC, CNRSMarne-la-ValléeFrance

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