Bounding the First Dirichlet Eigenvalue of a Tube Around a Complex Submanifold of a",P n (λ) in Terms of the Degrees of the Polynomials Defining It

被引：0

作者：

Domingo-Juan, M. Carmen ^{[1
]}

Miquel, Vicente ^{[2
]}

机构：

[1] Univ Valencia, Dept Matemat Econ & Empresa, Valencia 46022, Spain

[2] Univ Valencia, Dept Geometria & Topol, E-46100 Burjassot, Spain

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2014年 / 24卷 / 01期

关键词：

First Dirichlet eigenvalue; Tube around a complex submanifold of complex projective space; Spectral geometry; LAPLACE-BELTRAMI OPERATOR; RIEMANNIAN MANIFOLD; PROJECTIVE-SPACE; MEAN-CURVATURE; HYPERSURFACES; VOLUMES; DOMAINS;

D O I：

10.1007/s12220-012-9328-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold P of a",P (n) (lambda) which depends only on the radius of the tube, the degrees of the polynomials defining P, and the first eigenvalue of the tube around some model centers. The bounds are sharp on these models. Moreover, when the models used are a",P (q) (lambda) or Q (n-1)(lambda) these bounds also provide gap phenomena and comparison results.

引用

页码：92 / 103

页数：12