The spectrum of the Laplacian and volume growth of proper minimal submanifolds
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
The spectrum of the Laplacian and volume growth of proper minimal submanifoldsDate
2022-07Publisher
Springer-Verlag GmbH GermanyISSN
0025-5874; 1432-1823Bibliographic 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/s00209-022-02999-5Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
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
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- MAT_Articles [765]