Gromov-Hausdorff distance between a disk and a circle
2018年8月23日 · The Hausdorff distance between the closed unit disk $D^2$ of $\mathbb R^2$ (equipped with the standard Euclidean distance) and its boundary circle $S^1$ is obviously one.
For which metric spaces is Gromov-Hausdorff distance actually …
Front Note: Hanson's example works perfectly through a good correspondence (I failed to consider the case where $\infty$ is related to two elements that are pairs.) but I will keep the following up as a belabored example of bounded does not imply attains distance.
Applications of the notion of of Gromov-Hausdorff distance
Gromov's Theorem was, as far as I'm aware, the first but very far from the last application of Gromov–Hausdorff distance to group theory. One particularly fruitful line of reasoning starts with a sequence of actions of a group $\Gamma$ on (Gromov)-hyperbolic metric spaces.
Do continuous maps give continuity in the 'topology' of Hausdorff …
(Just recall that the Hausdorff distance between A and B is less than δ if and only if for any a∈A there is some b∈B with d(a,b)<δ and for any b∈B, there is some a∈A with d(a,b)<δ). PS: As to the topologic side of the question (stability of topological or homotopical properties of subsets of a space under perturbations in Hausdorff ...
Proving the inequality involving Hausdorff distance and …
2024年3月20日 · However this is such a typical example of wishful thinking that I believe it is worth leaving for the posterity. (I'll record it below as False Answer 2.) The right line of reasoning goes the other way around (take quasi-optimizers in the Hausdorff distance instead of taking a quasi-optimal plan).
reference request - Estimating the Hausdorff distance of parallel ...
2023年9月11日 · I haven't thought much about it, but maybe there's a way to prove this for strongly isomorphic polytopes and then approximate? This way there's a natural isomorphism between the vertex sets; if corresponding vertices are close enough then maybe the issues of adding/deleting points to compute the Hausdorff distance can be avoided.
pr.probability - Hausdorff distance is a lower (or upper bound) for ...
2018年9月9日 · For which metric spaces is Gromov-Hausdorff distance actually achieved? 2 Unconditional lower bound for volume of blowup $\mu(B^\epsilon)$ for $\mu(B) \in (0, 1)$ and $\epsilon > 0$ not "too large"
To minimize the Hausdorff distance between convex polygonal …
2019年9月1日 · Definition: The Hausdorff distance is the greatest of all the distances from a point in one set to the closest point in the other set. Question: Given two convex polygonal regions P1 and P2 on the plane, give an efficient algorithm that locates and orients P2 with respect to P1 (the two regions are allowed to overlap) so that the Hausdorff ...
Continuity of barycentre in Hausdorff metric - MathOverflow
Other such "reference points" which are Lipschitz-continuous w.r.t. the Hausdorff-distance, or w.r.t. some other metric (like the area of the symmetric difference) have been investigated. The objective is to get a fast heuristic or initial solution for matching two shapes under translation.
How to compute the Gromov-Hausdorff distance between spheres
2017年10月28日 · $\begingroup$ @Mark Sapir,Appreciate for help!I am reading the article you point out,it seems this article mainly focus on investigating the Gromov-Hausdorff limit space of a sequence of hyperbolic group equipped with modified G-H metric defined in 2.A with some special condition to ensure the limit space exists.and take a sequences corvarage to the limit …
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