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Results tagged with convex-geometry
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user 140709
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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vote
Accepted
Is the intrinsic volume always positive for maximum dimension?
$\DeclareMathOperator\dim{dim}$To answer my own question, I have put below a proof of both my conjectures (positivity and agreement with Hausdorff measure).
Let $A$ be a definable subset of $\mathbb{R …
- 509
4
votes
1
answer
236
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Is the intrinsic volume always positive for maximum dimension?
The intrinsic volume functions on $\mathbb{R}^d$ known from the Steiner formula and Hadwiger's Theorem can be extended to the domain of definable sets of an o-minimal structure $\text{Def}(\mathbb{R}^ …
- 509
4
votes
1
answer
184
views
Intrinsic volumes of non-polyconvex, non-compact sets
I am reposting this question I asked and bountied on Math SE, which has been upvoted but not answered or commented on.
The intrinsic volumes (AKA Minkowski Functionals or, with different normalizati …
- 509