Questions tagged [mg.metric-geometry]
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
9 questions from the last 7 days
16
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Is there a natural topology for sets of topological spaces?
The Gromov–Hausdorff metric makes a set of compact metric spaces into a metric space itself. I am wondering what some natural generalizations there are for arbitrary topological spaces. Namely, is ...
- 719
5
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1
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Can the Pythagorean theorem be proved using imaginary numbers?
Can the Pythagorean theorem be proved using imaginary numbers? The proof must avoid circular reasoning, of course.
I asked essentially the same question at MSE, but did not receive a definitive answer,...
- 3,577
2
votes
1
answer
155
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Converse of Scherk–Segre theorem on the number of vertices of a convex space curve
It is well known that any smooth simple closed convex curve $\gamma$ in $\mathbb{R}^{3}$ that meets no plane in more than 4 points has exactly 4 vertices, i.e., points of vanishing torsion; here "...
- 985
2
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1
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Does this result above six points follow have a name?
Does this result above six points follow have a name?
Let $A$, $B$, $C$, $D$, $E$, $F$ be six points in the plane and $AB, CF, ED$ are concurrent and $BC, DA, FE$ are concurrent then $CD, EB, AF$ ...
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-4
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0
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Is this a conclusion group for a new fundamental geometry problem? [closed]
Let σ(n) represent all possible values of the types of different lengths of segments connected to each other among n points in the definition,such as in the plane,σ(3)=(1,2,3),σ(3)min=1,in the ...
2
votes
0
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85
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Is there a natural topology for subsets of a fixed topological space?
This question is an extension/clarification of the question: Is there a natural topology for sets of topological spaces?
The Hausdorff distance assigns a distance to any two subspaces $X, Y$ of a ...
- 719
1
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0
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On $N$-partition of some common subsets $\Omega\subset\mathbb R^d$
Let $\Omega\subset\mathbb R^d$ be compact and convex, and denote by $\ell$ the normalised Lebesgue measure such that $\ell(\Omega)=1$. Let $N$ be an arbitrary but fixed integer.
In this post we set $d=...
- 1,399
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35
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Request for resources on directional derivative of the Riemannian distance function, and Berger's lemma about geodesics realizing the diameter
I've been recently interested in directional derivatives of the Riemannian distance function, and I came across this question, and its answer by Sergei Ivanov, where he stated an important result: (I ...
- 1,467
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0
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Longest TSP in the unitary disc
I have the unitary disc $D=\{(x,y) \in R^2: x^2 + y^2 \leq 1\} $, and an integer $n \geq 2$. I want to select $n$ points in $D$ to maximise the length shortest path that connects them all. In other ...
