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Results tagged with mg.metric-geometry
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user 64231
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
8
votes
Accepted
Distance function to a submanifold
I'm posting this sketch just for the sake of completeness. This question was already marked as answered by Anton. But I thought of this, more geometrical, argument after the discussion that answered t …
- 443
9
votes
2
answers
2k
views
Distance function to a submanifold
Let $M$ be a compact Riemannian manifold and $\Sigma\subset M$ a closed submanifold. Given $x\in M$ we define the distance function to $\Sigma$ by $$d_\Sigma(x):=\inf\{d(x,y):y\in \Sigma\},$$ where $d …
- 443