Contents Online
Mathematical Research Letters
Volume 18 (2011)
Number 1
Lower bounds on the Hausdorff measure of nodal sets
Pages: 25 – 37
DOI: https://dx.doi.org/10.4310/MRL.2011.v18.n1.a3
Authors
Abstract
Let $\ncal_{\phi_{\lambda}}$ be the nodal hypersurface of a $\Delta$-eigenfunction $\phi_{\lambda}$ of eigenvalue $\lambda^2$ on a smooth Riemannian manifold. We prove that $\hcal^{n-1}(\ncal_{\phi_{\lambda}}) \geq C \lambda^{\frac74-\frac{3n}4} $. %on the surface measure of its nodal set. The best previous lower bound was $e^{- C \lambda}$.
Published 28 February 2011