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

被引：11

作者：

Alencar, H ^{[1
]}

Do Carmo, M

Marques, F

机构：

[1] Univ Fed Alagoas, Dept Matemat, BR-57072900 Maceio, AL, Brazil

[2] IMPA, BR-22460320 Rio De Janeiro, Brazil

[3] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

ILLINOIS JOURNAL OF MATHEMATICS | 2001年 / 45卷 / 03期

关键词：

D O I：

10.1215/ijm/1258138155

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 delta. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to L-r when delta < 0.

引用

页码：851 / 863

页数：13

共 12 条

[1] STABLE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE
ALENCAR, H
DOCARMO, M
COLARES, AG
[J]. MATHEMATISCHE ZEITSCHRIFT, 1993, 213 (01) : 117 - 131
[2] Integral formulas for the r-mean curvature linearized operator of a hypersurface
Alencar, H
Colares, AG
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1998, 16 (03) : 203 - 220
[3] Alencar H., 1993, ANN GLOB ANAL GEOM, V11, P387, DOI DOI 10.1007/BF00773553
[4] Barbosa JLM, 1997, ANN GLOB ANAL GEOM, V15, P277
[5] BARBOSA L, 1988, MATH Z, V197, P123
[6] BARBOSA L, 1984, MATH Z, V195, P339
[7] ELSOUFI A, 1992, COMMENT MATH HELV, V67, P167
[8] GROSJEAN JF, 1995, CR ACAD SCI I-MATH, V321, P323
[9] Extrinsic upper bound for the first eigenvalue of elliptic operators defined on submanifolds and applications
Grosjean, JF
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (09): : 807 - 810
[10] EXTRINSIC UPPER-BOUNDS FOR GAMMA-1
HEINTZE, E
[J]. MATHEMATISCHE ANNALEN, 1988, 280 (03) : 389 - 402

← 1 2 →