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Results tagged with mg.metric-geometry
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user 129192
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
3
votes
1
answer
94
views
Finding particular closed paths in geometric plane regions
Let $X_m$ denote a set of $m\geq 3$ lines in $\mathbb{R}^2$ that are not all parallel. Consider the problem of determining a closed path of $kn$ points in $X_m$ $k, n \in \mathbb{Z}^+$, such that the …
- 1,087
1
vote
0
answers
95
views
Determining the behavior of a contraction mapping with undefined points
Label $X$ as the real interval $[0, a]$ where $a \in \mathbb{R}^+$, so that $\text{int}(X) = (0, a)$ labels the interior of $X$ and $\partial X$ labels the boundary of $X$. I have a function $f:\text …
- 1,087
0
votes
Accepted
Finding particular closed paths in geometric plane regions
The answer, given in this paper: https://arxiv.org/abs/2112.02207, turns out to be "yes", there always exist such closed curves. The theorem stating the answer to this question is given in the introd …
- 1,087