Title: Level sets of Neumann eigenfunctions

Authors: Rodrigo Banuelos and Michael M.H. Pang

Issue: Volume 55 (2006), Issue 3, 923-940

Abstract: 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.