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

9 votes
Accepted

Riemannian distance functions on the real line

[Moved from the comments/chat.] Define $D(x)$ by $$ \begin{align*} D(x) = \begin{cases} d(0,x), & \text{ if } x\geq 0;\\ -d(x,0), & \text{ if } x< 0. \end{cases} \end{align*} $$ Function $D(x)$ is n …
Yury's user avatar
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17 votes
Accepted

Efficiently determine if convex hull contains the unit ball

The problem is NP hard. Here is a proof sketch. The problem is to determine if there is a point $y$ with $\|y\|=1$ outside of the convex hull of given points $x_1,\dots, x_n$. Note that such point e …
Yury's user avatar
  • 726