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Results tagged with convex-geometry
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user 766
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
11
votes
0
answers
706
views
John-type theorems: trading structure for accuracy?
Given two symmetric convex bodies $B, B'$ in ${\bf R}^d$, define the Banach-Mazur distance $d(B,B')$ between them to be the least constant $\tau \geq 1$ such that
$$ B \subset TB' \subset \tau B$$
for …
- 4,653
33
votes
3
answers
2k
views
Polar body of a convex body that avoids a lattice
Let $K \subset {\bf R}^d$ be a symmetric convex body (an open bounded convex neighbourhood of the origin with $K = -K$) with the property that $K + {\bf Z}^d \neq {\bf R}^d$, i.e. the projection of $K …
- 4,713