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Keywords:
Lipschitz isomorphism; Hilbert space
Lipschitz isomorphism; Hilbert space
Summary:
We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?
References:
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[4] Klee V.L.: Convex Bodies and Periodic Homeomorphisms in Hilbert Space. Trans. Amer. Math. Soc. 74 (1953), no. 1, 10–43. DOI 10.1090/S0002-9947-1953-0054850-X | MR 0054850 | Zbl 0050.33202
[5] Nahum R.: On the Lipschitz equivalence of unit balls and spheres in normed spaces. preprint.
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