The “hot spots” conjecture for domains with two axes of symmetry

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Geometrical Structure of Laplacian Eigenfunctions (2012, background): “This conjecture was proved by Banuelos and Burdzy for a class of planar domains [41] but in general the statement is wrong, as shown by several counter-examples [54, 102, 104, 257].”
The hot spots problem in planar domains with one hole (2004, result): “in. The conjecture is false at this level of generality (see [BB2] and [BW]) but Research partially supported by NSF grant DMS-0303310. 1 it is true for some classes of domains (see [A], [AB], [BB1], [JN], [K], [P]). The counterexample given in [BW] is a planar domain with two holes and it suggests,”
On Neumann eigenfunctions in lip domains (2004, background): “Our main result solves two problems posed by Jerison and Nadirashvili ([14]).”
The legacy of Vladimir Andreevich Steklov (2014, background): “This relationship between the two problems implies, in particular, that the results obtained in [3] and [26] for planar convex domains with two orthogonal axes of symmetry (e.”
A Berry-Esseen type inequality for convex bodies with an unconditional basis (2007, background): “, Burdzy [10], Jerison and Nadiras hvili [19] and references therein.”