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

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Distance from a hyperplane (determined by the cut of a convex cone with the unit sphere) to ...

The setting is a convex cone $C$ in $\mathbb{R}^d$ with the property that if you cut it with $S^d$ the volume of the cut is greater than or equal to $\operatorname{Vol}(S^d)/d+1$. That is, the volume …
Mario Roberts's user avatar