Timeline for Riemannian manifolds with a unique distance property
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2023 at 10:56 | comment | added | Chris H | Yea having very few possibilities for maximal distance $k$ tuples would probably be more flexible. The examples I had in mind also had a kind of nondegeneracy, where one can complete $i$ tuples to $k$ tuples, but I’d be interested in either case. Even for say, graphs I’d be curious what this property resembles. | |
| Jun 9, 2023 at 7:46 | comment | added | Sebastian Goette | Is it possible to construct Riemannian manifolds of diameter $1$ where there is exactly one $k$-element set of points having pairwise distance $1$, maybe already surfaces? If yes, I would expect that these manifolds can be deformed a bit in some open subset not hitting any of the connecting arcs without losing that property. | |
| Jun 7, 2023 at 16:55 | comment | added | C.F.G | Is this property related to the q-extent of a metric space X which is the maximum average distance between q points in X? i.e. $xt_q(X):=\max_{x_1,\dots,x_q}xt_q(x_1 ,\dots ,x_q)$ where $xt_q(x_1 ,\dots,x_q) = {q\choose 2}^{-1}\sum_{i<j} \operatorname{dist}(x_i , x_j) .$ | |
| Jun 7, 2023 at 11:03 | history | asked | Chris H | CC BY-SA 4.0 |