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Füredi–Lagarias–Morgan exponential bound for equilateral sets in strictly convex spaces

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Let XX be a strictly convex nn-dimensional Minkowski space. Füredi–Lagarias–Morgan conjecture. There exists some constant ε>0\varepsilon>0 such that

e(X)≤(2−ε)n.e(X)\leq (2-\varepsilon)^n.

The conjecture would improve the general upper bound for equilateral sets in strictly convex normed spaces. The source does not indicate whether it has been resolved.

References

Primary source

Konrad J. Swanepoel, “Equilateral sets in finite-dimensional normed spaces”, arXiv:math/0406264 (2004).

equilateral-setsnormed-spacesstrictly-convex-spaces
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