# Tagged Questions

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

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### Ascertain properties of a new kind of rectilinear-convex set

PREABMLE TO MY QUESTION I am reading about convex sets and hulls in orthogonal/rectilinear spaces. As can be seen in this publication, for a given set of points in $\mathbb{R}^{2}$, there are many ...
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### Extremal Lipschitz convex functions

Let $B_d$ the unit ball in $\mathbb{R}^d$, and let $F_d$ be the set of convex functions with Lipschitz constant at most 1 from $B_d$ to $\mathbb{R}$. When $d=1$ (so the domain is the just the ...
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### Decidability of convex rearrangements of polygons

Triggered by the MO question, "How many convex shapes can be made with the pieces of the Stomachion?," I would like to pose this question: Q. Given $n$ polygons in a set $S$, say each with integer ...
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### On convergence of convex bodies

Let $K\subset \mathbb{R}^n$ be a compact convex set of full dimension. Assume that $0\in \partial K$. Question 1. Is it true that there exists $\varepsilon_0>0$ such that for any ...
Let consider a surface $z=1/(xy)$ and a sphere defined by $(x-1.5)^2+(y-1.5)^2+(z-1.5)^2=3/4$. The sphere touches the surface at (1,1,1). Is it possible to prove that point (1,1,1) is the only ...