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Results tagged with mg.metric-geometry
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user 30800
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
5
votes
Continuity of barycentre in Hausdorff metric
This question has been first discussed in the paper [ABB] below. They show that, in the plane, the barycenter of the boundary has the desired property: It is Lipschitz-continuous with respect to the …
- 1,083
2
votes
Which 4D point groups force an isotropic moment of inertia?
If the object does not have an isotropic moment of inertia, then its symmetry group must be reducible in the language of group representations, i.e., a direct sum of lower-dimensional representations. …
- 1,083
4
votes
Accepted
Intersection of Cones in Three Space
I am not sure I understand the question, see the remarks of Qfwfq. Here is something related which might nevertheless be interesting for some branches of applied mathematics: an algorithm for paramete …
- 1,083
2
votes
Accepted
Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equali...
Here is a sketch of an answer that involves the squared Euclidean distances between the four points $A,B,C,D$ (and only the squared ones, not a mixture between squared and non-squared distances.)
Sup …
2
votes
Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equali...
No. (This was an answer to a previous, not entirely clear version of the problem.) Take an equilateral triangle ABC of side length 1, plus the midpoint D of the side AC.
By pushing D slightly in or ou …
- 1,083
1
vote
Accepted
Expected minimum face angle of random convex polyhedron in $\mathbb{R}^3$
The answer is YES. (I am assuming you mean the angle between two adjacent edges on a common face. (The dihedral angles all go to $\pi$.)) The easy and brief reason is that, in a large random point set …
- 1,083