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Results tagged with convex-geometry
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user 1044
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
5
votes
Accepted
A min-max formula for depth of the origin in a convex set
My office is quieter this morning, so let's try again. I'll assume that $C$ is compact with $0 \in \operatorname{int} C$. Let $B_r$ denote the ball of radius $r$ centered at $0$. Then
$\operatorname …
- 11.4k
3
votes
Accepted
Diameter of a metric on orbits under affine bijections of $n-$dimensional convex compact sets
I assume you also want your compact sets to have non-empty interior, hence positive volume.
The literature mostly deals with the related Banach-Mazur metric $d_{BM}(A,B)$, in which it is assumed that …
- 11.4k
11
votes
Accepted
Concentration of measure for arbitrary convex bodies?
There are many results, and an active research industry, along these lines. In general the Euclidean ball is the best-behaved convex body in this respect, and just how similar an arbitrary convex bod …
- 11.4k
5
votes
Accepted
A question on the Mahler conjecture
No, it is not known that the minimum is unique, but it is believed to be. In fact, this paper by Kim and Reisner proves that the simplex is (modulo linear equivalence) a strict local minimum; thus th …
- 11.4k