Abstract

We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold $M$. As an application we consider the question of approximating points on $M$ by nodal sets, and explore analogy with approximation by rational numbers.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1109-1135
Launched on MUSE
2009-07-23
Open Access
No
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