Is it true that for every imbedding of an n-torus T^n in any Euclidean m-space satisfies ∫ |H|^n dV ≥ (4/n)^(n/2) π^n?

07 January 2016 1 4K Report

In my question given above, H is the mean curvature of the imbedded n-torus in the Euclidean m-space with arbitrary codimension.

Bang-Yen Chen

The answer to this question is yes when n=2 and m=3 (see [F.C. Marquesand A. Neves, Min-max theory and the Willmore conjecture. Ann. of Math. 179 (2014), no. 2, 683–782]).

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