2 problems

Let $X\subset {\mathbb R}^{n+1}$ be a convex surface equipped with its standard DC structure, and call a DC structure compatible with the intrinsic metric if its charts are locally…

Let $X$ be a convex surface in ${\mathbb R}^{n+1}$, let $x_0\in X$ be fixed, and consider the distance function $x\mapsto {\rm dist}(x,x_0)$. For $n=1$, this function is DC on all…