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Results tagged with convex-geometry
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user 169474
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
0
votes
Center of convex figure
Almost complete proof (the final argument still needs to be formalized).
We work in any Euclidean space $E$.
Informally, I take $p_F$ equal to the center of the closed ball with minimum radius contain …
- 3,808
2
votes
Accepted
Norm functions induced by convex bodies
I think you need to assume that $K$ has a smooth boundary and is strictly convex to ensure that $g$ and $h$ are differentiable outside $0$.
Anyway, I do not think that the result is true. Assume that …
- 3,808
2
votes
Convex functions in convex sets
Not an answer, but a too long remark for a comment.
The property holds for any Euclidean ball. By translation one may assume that the center is $0$. Call R the radius. Then the volume is $b_nR^n$ and …
- 3,808