Resumen de Tubular neighborhoods of nodal sets and diophantine approximation

Dmitry Jakobson, Dan Mangoubi

• 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.