<< The hotspots conjecture can be expressed in simple English as: Suppose a flat piece of metal, represented by a two-dimensional bounded connected domain R, is given a generic initial heat distribution which then flows throughout the metal. Assuming the metal is insulated (i.e. no heat escapes from the piece of metal), then at all sufficiently large times, the hottest and coldest points on the metal both will lie on its boundary... . . . This conjecture has been proven for some domains and disproven for others. It is conjectured by Rodrigo Banuelos for any bounded simply-connected planar domain. . . . I point out this conjecture is "obviously false" in any dimension>=1 for a rotationally-symmetric ball. PROOF: start with generic rotationally symmetric heat distribution. (Hence eternally is rotationally symmetric.) At all future times, temperature is same everywhere on the boundary. Hence conjecture that the boundary includes the hottest point, contradicts conjecture it includes the coldest point.

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Why is the constant distribution excluded? --Dan ________________________________________________________________________________________ It goes without saying that .