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Answer by Anton Petrunin for Derivative of distance function to a convex set...
It is true.First part.Assume $x\notin C$, note that $\mathrm{dist}_{\pi(x)}\ge\mathrm{dist}_{C}$.It follows that$$d_x\mathrm{dist}_{C}(v) \le d_x\mathrm{dist}_{\pi(x)}(v)= -\langle \uparrow_x^{\pi(x)},...
View ArticleDerivative of distance function to a convex set in CAT(0) space
Let $(X,d)$ be a complete CAT(0) space. We denote by $T_x X$ the tangent cone at a point $x\in X$ and by $d_x$ its associated distance. So $(T_x X,d_x)$ is also a complete CAT(0) space. In CAT(0)...
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