Level Sets of Neumann Eigenfunctions
Rodrigo Bañuelos, Michael M. H. Pang · Indiana University Mathematics Journal · 2006
In this paper we prove that the level sets of the first non-constant eigenfunction of the Neumann Laplacian on a convex planar domain have only finitely many connected components. This problem is motivated, in part, by the hot spots conjecture of J. Rauch.