Tubular neighborhoods of nodal sets and diophantine approximation

Dmitry Jakobson*, Dan Mangoubi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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..

Original languageAmerican English
Pages (from-to)1109-1135
Number of pages27
JournalAmerican Journal of Mathematics
Volume131
Issue number4
DOIs
StatePublished - Aug 2009
Externally publishedYes

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