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2012 A natural lower bound for the size of nodal sets
Hamid Hezari, Christopher Sogge
Anal. PDE 5(5): 1133-1137 (2012). DOI: 10.2140/apde.2012.5.1133

Abstract

We prove that, for an n-dimensional compact Riemannian manifold (M,g), the (n1)-dimensional Hausdorff measure |Zλ| of the zero-set Zλ of an eigenfunction eλ of the Laplacian having eigenvalue λ, where λ1, and normalized by M|eλ|2dVg=1 satisfies

C | Z λ | λ 1 2 M | e λ | d V g 2

for some uniform constant C. As a consequence, we recover the lower bound |Zλ|λ(3n)4.

Citation

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Hamid Hezari. Christopher Sogge. "A natural lower bound for the size of nodal sets." Anal. PDE 5 (5) 1133 - 1137, 2012. https://doi.org/10.2140/apde.2012.5.1133

Information

Received: 12 August 2011; Accepted: 24 October 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1329.35224
MathSciNet: MR3022851
Digital Object Identifier: 10.2140/apde.2012.5.1133

Subjects:
Primary: 35P15

Rights: Copyright © 2012 Mathematical Sciences Publishers

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