Upper bounds for the first eigenvalue of the operator Lr and some applications

Hilário Alencar; Manfredo Do Carmo; Fernando Marques

doi:10.1215/ijm/1258138155

Upper bounds for the first eigenvalue of the operator L_r and some applications

Hilário Alencar, Manfredo Do Carmo, Fernando Marques

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We obtain upper bounds for the first eigenvalue of the linearized operator L_r of the r-mean curvature of a compact manifold immersed in a space of constant curvature δ. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to L_r when δ < 0.

Original language	English (US)
Pages (from-to)	851-863
Number of pages	13
Journal	Illinois Journal of Mathematics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1258138155
State	Published - 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Upper bounds for the first eigenvalue of the operator Lr and some applications",

abstract = "We obtain upper bounds for the first eigenvalue of the linearized operator Lr of the r-mean curvature of a compact manifold immersed in a space of constant curvature δ. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to Lr when δ < 0.",

author = "Hil{\'a}rio Alencar and {Do Carmo}, Manfredo and Fernando Marques",

year = "2001",

doi = "10.1215/ijm/1258138155",

language = "English (US)",

volume = "45",

pages = "851--863",

journal = "Illinois Journal of Mathematics",

issn = "0019-2082",

publisher = "Duke University Press",

number = "3",

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T1 - Upper bounds for the first eigenvalue of the operator Lr and some applications

AU - Alencar, Hilário

AU - Do Carmo, Manfredo

AU - Marques, Fernando

PY - 2001

Y1 - 2001

N2 - We obtain upper bounds for the first eigenvalue of the linearized operator Lr of the r-mean curvature of a compact manifold immersed in a space of constant curvature δ. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to Lr when δ < 0.

AB - We obtain upper bounds for the first eigenvalue of the linearized operator Lr of the r-mean curvature of a compact manifold immersed in a space of constant curvature δ. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to Lr when δ < 0.

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U2 - 10.1215/ijm/1258138155

DO - 10.1215/ijm/1258138155

M3 - Article

AN - SCOPUS:0039248480

SN - 0019-2082

VL - 45

SP - 851

EP - 863

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 3

ER -

Upper bounds for the first eigenvalue of the operator L_r and some applications

Abstract

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