# Questions tagged [mg.metric-geometry]

Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces.

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### What do you call this notion of similarity between subsets of a metric space?

Given a metric space $X$, we say a continuous isometry is a continuous map $F:X\times[0,1]\to X$ such that defining $f_t(x) = F(x,t)$ for $t \in [0,1]$, we have that $f_0$ is the identity map and $f_t$...
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### Minimize the z coordinate for the intersection of two extrusions of coplanar circles along parametric paths

Sorry if my question isn't phrased as formally as it should be; this is my first math question on any online forum. I basically want to minimize the z coordinate of the intersection of some number of ...
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### intersection and self intersection on non compact complex surfaces

I'd like to have a definition of intersection on non compact complex surfaces because all i have found so far is only about projective surfaces. for example how can i define the self intersection of ...
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### Construct by compactness (Pentagonal tiling – Rao paper)

In the (arxiv) paper, Exhaustive search of convex pentagons which tile the plane, on page 4 under the proof of Lemma 2, it is said that: "... We keep a connected component $H_d'$ of $H_{d}$ such ...
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### Which unfoldings of the $d$-dimensional hypercube tile $(d{-}1)$-space?

A six year old question, Which unfoldings of the hypercube tile $3$-space?, has just been answered by Moritz Firsching: All $261$ unfoldings tile space! So now we know: For $d=2$, the unfolding of ...
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### Gromov–Hausdorff closure of non-positively curved graphs

Setup: Let $\Gamma$ be the set of non-positively curved weighted connected graphs, with finitely many points, which are isometrically embedded in $\mathbb{R}^n$; for some $n\in \mathbb{N}$;$n\geq 2$. ...
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### Thirteen-point conic and four-point line, are they new?

We know that Five points determine a conic and Two Points Determine a Line. Here I found a simple construct of a conic through $7$ points (in PS I note that how the conic through thirteen points) and ...
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Let $M$ be a non compact complex surface and S an embedded compact Riemann surface in $M$. I already know how to show the following equality of fiber bundle: $$\Omega^2_{M}|S =\Omega^1_S \otimes N^*_S... 0answers 90 views ### Are there examples of hyperbolic manifolds with finite Bowen-Margulis measure and fundamental group which is not relatively hyperbolic? It is well known that a geometrically finite hyperbolic manifold (quotient of H^n) has finite Bowen-Margulis measure. Marc Peigné [1] constructed examples of geometrically infinite hyperbolic ... 0answers 54 views ### Distance Metric on a Polytope Primary Question: Is it possible to define a distance metric on a polytope (or permutohedron in particular)? I am aware that neither is a smooth, Riemannian manifold; however, computer scientists have ... 1answer 62 views ### A generalized norm function in \mathbb{R}^n [closed] We defined a new norm. The norm of x \in \mathbb{R}^n is defined as$$ N_P(x) = \min \{t \geq 0 : x \in t\cdot P\} \enspace, where $P$ is a centrally symmetric and convex body centered at the ...
Let $S$ be a finite set of points in $\mathbb{R}^{d}$, $c(s) \in [0,1]$ such that $\sum_{s \in S} c(s) = 1$, $\rho$ continuous and non-vanishing probability distribution on $[0,1]^{d}$ and $\mu$ ...
A fugitive is surrounded by $N$ police officers, with the nearest one at distance $1$ away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than ...