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Strong Isotropic Constant Conjecture

The strong isotropic constant conjecture asserts that the isotropic constant L_K of a convex body K subset R^n is at most the simplex value,

L_K<=((n!)^(1/n))/((n+1)^((n+1)/(2n))sqrt(n+2)).

It strengthens the question of a dimension-independent upper bound by specifying the sharp value in every dimension.

See also

Convex Body, Differential Entropy, Isotropic Constant, Mahler Volume Product Conjecture, Simplex

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References

Kipp, C. "Shadow Systems, Decomposability and Isotropic Constants." Disc. Comput. Geom. 76, 1391-1425, 2026. https://doi.org/10.1007/s00454-026-00829-7.

Cite this as:

Weisstein, Eric W. "Strong Isotropic Constant Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrongIsotropicConstantConjecture.html

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