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Tubular Neighborhoods of Nodal Sets and Diophantine Approximation
classification
🧮 math.SP
math.DG
keywords
nodalapproximationsetstubularanalogyanalyticapplicationapproximating
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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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