scholarly journals Pleijel’s nodal domain theorem for Neumann and Robin eigenfunctions

2019 ◽  
Vol 69 (1) ◽  
pp. 283-301
Author(s):  
Corentin Léna
Keyword(s):  
Nodal Domain

On the Inner Radius of a Nodal Domain

2008 ◽  
Vol 51 (2) ◽  
pp. 249-260 ◽  
Author(s):  
Dan Mangoubi
Keyword(s):  
Riemannian Manifold ◽  
Lower Bounds ◽  
Type Inequality ◽  
Large Eigenvalue ◽  
Upper And Lower Bounds ◽  
Local Behavior ◽  
Nodal Domain ◽  
Closed Riemannian Manifold ◽  
Inner Radius

AbstractLet M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λα(log λ)β. Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman and a Poincaré type inequality proved by Maz’ya. Sharp lower bounds are known only in dimension two. We give an account of this case too.

scholarly journals Discrete nodal domain theorems

2001 ◽  
Vol 336 (1-3) ◽  
pp. 51-60 ◽  
Author(s):  
E. BrianDavies ◽  
GrahamM.L. Gladwell ◽  
Josef Leydold ◽  
Peter F. Stadler
Keyword(s):  
Nodal Domain

scholarly journals Spectrum of Signless 1-Laplacian on Simplicial Complexes

10.37236/8951 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Xin Luo ◽  
Dong Zhang
Keyword(s):  
Chromatic Number ◽  
Spectral Theory ◽  
Independence Number ◽  
Simplicial Complexes ◽  
Nodal Domain ◽  
Largest Eigenvalue ◽  
Cheeger Constant ◽  
Laplacian Eigenvalues ◽  
Combinatorial Properties ◽  
Sandwich Theorem

We introduce the signless 1-Laplacian and the dual Cheeger constant on simplicial complexes.  The connection of its spectrum to the combinatorial properties like independence number,  chromatic number and dual Cheeger constant is investigated. Our estimates  can be comparable to Hoffman's bounds on Laplacian eigenvalues of simplicial complexes. An interesting inequality involving multiplicity of the largest eigenvalue, independence number and chromatic number is provided, which could be regarded as a variant version of Lovász sandwich theorem. Also, the behavior of 1-Laplacian under the topological operations of wedge and duplication of motifs is studied. The Courant nodal domain theorem in spectral theory is extended to the setting of signless 1-Laplacian on complexes.

scholarly journals Nodal domain and eigenvalue multiplicity of graphs

2012 ◽  
Vol 3 (4) ◽  
pp. 609-622 ◽  
Author(s):  
Hao Xu ◽  
Shing-Tung Yau
Keyword(s):  
Nodal Domain

A nodal domain property for the p-Laplacian

2000 ◽  
Vol 330 (8) ◽  
pp. 669-673 ◽  
Author(s):  
Mabel Cuesta ◽  
Djairo G. De Figueiredo ◽  
Jean-Pierre Gossez
Keyword(s):  
Nodal Domain ◽  
Domain Property
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