Tubular neighbourhoods, cone conditions and inradius estimates
Bogdan Georgiev, Mayukh Mukherjee · arXiv (Cornell University) · 2016
We give asymptotic upper and lower bounds on the volume of a tubular neighbourhood of the nodal set of a Laplace eigenfunction on a smooth closed Riemannian manifold. We derive an analogue of a result of Cheng in higher dimensions regarding the interior opening angle of a nodal domain at a singular point. Lastly, we give some quantitative estimates for radii of inscribed balls in nodal domains on which the eigenfunction satisfies exponentially small $L^\infty$ bounds.