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Lower Bounds for Nodal Sets of Dirichlet and Neumann Eigenfunctions

Lower Bounds for Nodal Sets of Dirichlet and Neumann Eigenfunctions Let $${\phi}$$ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set $${\{\phi = 0\}}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

Lower Bounds for Nodal Sets of Dirichlet and Neumann Eigenfunctions

Communications in Mathematical Physics , Volume 317 (3) – Aug 18, 2012

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer-Verlag
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Statistical Physics, Dynamical Systems and Complexity; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
DOI
10.1007/s00220-012-1554-4
Publisher site
See Article on Publisher Site

Abstract

Let $${\phi}$$ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set $${\{\phi = 0\}}$$ .

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Aug 18, 2012

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