SPECTRUM OF THE COMPLEX LAPLACIAN ON PRODUCT DOMAINS

被引：8

作者：

Chakrabarti, Debraj ^{[1
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 09期

关键词：

DERIVATIVE-NEUMANN PROBLEM;

D O I：

10.1090/S0002-9939-10-10522-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the spectrum of the complex Laplacian square on a product of Hermitian manifolds is the Minkowski sum of the spectra of the complex Laplacians on the factors. We use this to show that the range of the Cauchy-Riemann operator (partial derivative) over bar is closed on a product manifold, provided it is closed on each factor manifold.

引用

页码：3187 / 3202

页数：16

共 50 条

[1] ON THE NEGATIVE SPECTRUM OF THE ROBIN LAPLACIAN IN CORNER DOMAINS
Bruneau, Vincent
Popoff, Nicolas
[J]. ANALYSIS & PDE, 2016, 9 (05): : 1259 - 1283
[2] The spectrum of large powers of the Laplacian in bounded domains
Katzav, E.
Adda-Bedia, M.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (02)
[3] Complex powers of the Neumann Laplacian in Lipschitz domains
Mendez, O
Mitrea, M
[J]. MATHEMATISCHE NACHRICHTEN, 2001, 223 : 77 - 88
[4] The signless Laplacian spectrum of rooted product of graphs
Maghsoudi, Maryam
Heydari, Abbas
[J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2018, 10 (06)
[5] Another estimation of Laplacian spectrum of the Kronecker product of graphs
Basic, Milan
Arsic, Branko
Obradovic, Zoran
[J]. INFORMATION SCIENCES, 2022, 609 : 605 - 625
[6] SPECTRUM THEORY OF LAPLACIAN IN UNBOUNDED DOMAINS CONTAINING CYLINDERS AND CONES
GUILLOT, JC
WILCOX, CH
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (19): : 1171 - 1174
[7] The *-product of domains in several complex variables
Zajac, Sylwester
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2022,
[8] The *-product of domains in several complex variables
Zajac, Sylwester
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024, 69 (01) : 35 - 46
[9] An Alternative Technique to Find the Spectrum and Laplacian Spectrum of a Cartesian Product of Signed Graphs
Kaur, Bableen
Kumar, Sandeep
Sinha, Deepa
[J]. NATIONAL ACADEMY SCIENCE LETTERS-INDIA, 2024, 47 (04): : 405 - 417
[10] Inequalities for eigenvalues of Laplacian on domains and compact complex hypersurfaces in complex projective spaces
Cheng, Qing-Ming
Yang, Hongcang
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2006, 58 (02) : 545 - 561

← 1 2 3 4 5 →