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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

8 votes

Are there smooth bodies of constant width?

Take any odd smooth function h on the unit (d-1)-sphere and take a constant r>0 large enough to ensure that h+r is the support function of a convex body K (the condition for h+r to be the support fun …
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