We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with ...

Fernando Soria, Examples and Counterexamples to a Conjecture in the Theory of Differentiation of Integrals, Annals of Mathematics, Vol. 123, No. 1 (Jan., 1986), pp. 1-9 ...