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    • A counterexample to the "hot spots" conjecture 

      Burdzy, Krzysztof; Werner, Wendelin (Princeton University and Institute for Advanced Study, 1999-01)
      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 Neumann boundary conditions ...
    • On the "hot spots" conjecture of J. Rauch 

      Burdzy, Krzysztof; Banuelos, Rodrigo (Academic Press (Elsevier), 1999-05-10)
      We will state several rigorous versions of J. Rauch's "hot spots" conjecture, review some known results, and prove the conjecture under some additional assumptions. Let us, however, first observe that the conclusion ...