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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Regularity of the Minkowski functionnal of a convex

Let $K$ be a convex compact set in $\mathbb{R}^2$ with $0 \in \overset{\circ}{K}$. The Minkowski functional associated to K is: \begin{align*} \varphi_K(x):= \inf \left\{t>0 \; : \; tx \in K \right\ …