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Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds

Annals of Global Analysis and Geometry volume 62, pages 489–505 (2022)Cite this article

Abstract

We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds of bounded sectional curvature endowed with a weighted measure.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, Brazil

    Fernando Manfio

  2. Laboratoire d’Analyse et de Mathématiques Appliquées, UPEM-UPEC, CNRS, 77454, Marne-la-Vallée, France

    Julien Roth

  3. School of Mathematice and Computer Science, Indian Institute Of Technology Goa, Ponda, 403401, India

    Abhitosh Upadhyay

Authors
  1. Fernando Manfio
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  2. Julien Roth
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  3. Abhitosh Upadhyay
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Correspondence to Abhitosh Upadhyay.

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The first author is supported by Fapesp, Grant 2019/23370-4 and the third author gratefully acknowledges the financial support from the Indian Institute of Technology Goa through Start-up Grant 2021/SG/AU/043.

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Manfio, F., Roth, J. & Upadhyay, A. Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds. Ann Glob Anal Geom 62, 489–505 (2022). https://doi.org/10.1007/s10455-022-09862-0

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  • DOI: https://doi.org/10.1007/s10455-022-09862-0

Keywords

  • Submanifolds
  • Reilly-type upper bounds
  • Eigenvalues estimates
  • Divergence-type operators
  • Steklov problems

Mathematics Subject Classification

  • 53C24
  • 53C42
  • 58J50