The spectrum of the Laplacian and volume growth of proper minimal submanifolds

Thumbnail
View/Open
Bessa_2022_Spectrum.pdf (221.8Kb)
Impact
Share
Show METS | MarcXML
Export to
Export to Mendeley
Metadata
Show full item record

comunitat-uji-handle:10234/9

comunitat-uji-handle2:10234/7037

comunitat-uji-handle3:10234/8635

comunitat-uji-handle4:

INVESTIGACION

Metadata

Title
The spectrum of the Laplacian and volume growth of proper minimal submanifolds
Author (s)
 Bessa, G. Pacelli;
 Gimeno, Vicent;
 Polymerakis, Panagiotis
Date
2022-07
Publisher
Springer-Verlag GmbH Germany
URI
http://hdl.handle.net/10234/200393
DOI
https://doi.org/10.1007/s00209-022-02999-5
ISSN
0025-5874; 1432-1823
Bibliographic citation
Bessa, G.P., Gimeno, V. & Polymerakis, P. The spectrum of the Laplacian and volume growth of proper minimal submanifolds. Math. Z. 301, 2761–2770 (2022). https://doi.org/10.1007/s00209-022-02999-5
Type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Subject
Abstract
We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of Rn in terms of their volume growth. Our result can be viewed as an extrinsic version of Brooks’s essential ... [+]
We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of Rn in terms of their volume growth. Our result can be viewed as an extrinsic version of Brooks’s essential spectrum estimate (Brooks, Math Z 178(4): 501–508, 1981, Thm. 1) and it gives a fairly general answer to a question of Yau (Asian J Math 4(1): 235– 278, 2000) about upper bounds for the first eigenvalue (bottom of the spectrum) of immersed minimal surfaces of R3. [-]
Is part of
Mathematische Zeitschrift, Vol. 301 (2022)
Funder Name
CNPq-Brazil | Universitat Jaume I | DGI -MINECO (FEDER) | Max Planck Institute for Mathematics (Bonn)
Project code
303057/2018-1 | P1-1B2012-18 | MTM2013-48371-C2-2-P
Project title or grant
Isoperimetría extrínseca, crecimiento del volumen y topología de subvariedades en una variedad con un polo. Aplicaciones a la teoría de la información cuántica | Análisis geométrico y aplicaciones
Rights
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
Except where otherwise noted, this item's license is described as © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022