Tubular neighborhoods of nodal sets and diophantine approximation

• Autores: Dmitry Jakobson, Dan Mangoubi
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 131, Nº 4, 2009, págs. 1109-1135
• Idioma: inglés
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• Resumen

  • 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.