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October 2015 Eigenfunctions with prescribed nodal sets
Alberto Enciso, Daniel Peralta-Salas
J. Differential Geom. 101(2): 197-211 (October 2015). DOI: 10.4310/jdg/1442364650

Abstract

In this paper we consider the problem of prescribing the nodal set of low-energy eigenfunctions of the Laplacian. Our main result is that, given any separating closed hypersurface $\Sigma$ in a compact $n$-manifold $M$, there is a Riemannian metric on $M$ such that the nodal set of its first nontrivial eigenfunction is $\Sigma$. We present a number of variations on this result, which enable us to show, in particular, that the first nontrivial eigenfunction can have as many non-degenerate critical points as one wishes.

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Alberto Enciso. Daniel Peralta-Salas. "Eigenfunctions with prescribed nodal sets." J. Differential Geom. 101 (2) 197 - 211, October 2015. https://doi.org/10.4310/jdg/1442364650

Information

Published: October 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1328.53046
MathSciNet: MR3399096
Digital Object Identifier: 10.4310/jdg/1442364650

Rights: Copyright © 2015 Lehigh University

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Vol.101 • No. 2 • October 2015
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