# New extremal domains for the first eigenvalue of the Laplacian in flat tori

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Lets? N0 and let ?be the set of functionsxdefined on a finite intervalIand such that, for all collections ofs+1 pairwise different pointst0,...,ts ?I,the corresponding divided differences [x;t0,...,ts] of ordersare nonnegative. Let ?Bp ? ??Bp, 1 =p= 8 whereBp is a unit ball in the spaceLp,and...