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Results tagged with mg.metric-geometry
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user 51695
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
0
votes
Accepted
Distance function and geometry of the set
Since Pietro Majer definitely was right about the structure of the set but hasn't supplied a proof let me jump in with an elementary one. I think the problem is to specific to find a reference, but it …
- 2,504
2
votes
Vector measures as metric currents
To me your definition seems to be the right one, you just need to prove that it is well defined when approximating Lipschitz with $C^1$-functions. For that you probably need the distributional diverge …
- 2,504
3
votes
When is a bi-Lipschitz homeomorphism smoothable?
There is some interest in a related question in non-linear elasticity, specifically people there would consider a function "smoothable" if there is a close-by (in some norm applying both to function a …
- 2,504
1
vote
Can you measure the degree of uniformity of a 2d shape?
Assuming that your shape has a nice enough description in polar coordinates, the Fourier-series might help you. Specifically, assume that the center of gravity of your shape is in $0$ and it can be wr …
- 2,504
3
votes
Can I find $n$ points on the boundary of an $n$-dimensional ball with certain properties?
It is not possible for $n>2$.
Pick any point $v$ and consider the cone spanned by all tangent rays. Clearly that cone has to be a subset of the solution, as otherwise you would miss part of the ball. …
- 2,504
3
votes
Accepted
Fast algorithms for calculating the distance between measures on finite ultrametric spaces
This is a rather more fun problem than I thought. I must apologize though, as your question is a reference request and I have no references apart from pointing at any textbook on discrete optimization …
- 2,504