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Results tagged with mg.metric-geometry
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user 151664
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
1
vote
Conditions on a parametric curve so that its normal plane covers R^n
For a point $x \in \mathbb{R}^n$, saying that $x$ lies on the normal plane at $p(s^*)$ is equivalent to saying that $s^*$ is a critical point for the distance function between $x$ and $p(s)$.
If your …
- 1,277
1
vote
Hausdorff metric selectors
No such selector exists. Retooling my comment above, let $G$ be the open interval $(-1,1)$. Take $\epsilon>0$ such that $\ \epsilon<\min(1-s(G), s(G)-1)\ $ hence the closed $\epsilon$-neighborhood of …
- 1,277
0
votes
Unbounded curvature implies infinite diameter on complete metric spaces
If you want something smoother, you can try an example like the surface in $\mathbb{R}^3$ given in spherical coordinates by $\rho=\text{exp}(-\theta)$ for $\theta \ge 0$. This kind of looks like a cla …
- 1,277