Abstract
We prove that, for an -dimensional compact Riemannian manifold , the -dimensional Hausdorff measure of the zero-set of an eigenfunction of the Laplacian having eigenvalue , where , and normalized by satisfies
for some uniform constant . As a consequence, we recover the lower bound .
Citation
Hamid Hezari. Christopher Sogge. "A natural lower bound for the size of nodal sets." Anal. PDE 5 (5) 1133 - 1137, 2012. https://doi.org/10.2140/apde.2012.5.1133
Information