Tubular Neighborhoods of Nodal Sets and Diophantine Approximation

Details Tubular Neighborhoods of Nodal Sets and Diophantine Approximation Tubular Neighborhoods of Nodal Sets and Diophantine Approximation

2007-07-27

arxiv.org/abs/0707.4045v2

Amer. J. Math. 131 (2009), no. 4, 1109--1135.

Mathematics

Spectral Theory

22 pages; revised version containing full proof of lower bound; reference added; to appear in Amer. J. Math.

Scientific paper

10.1353/ajm.0.0066

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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