All Questions
3 questions
10
votes
2
answers
751
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On Gromov's proof of the systolic inequality $\operatorname{Sys}_1(M)\leq 6\operatorname{FillRad}(M)$
In the page 10 of the paper "Filling Riemannian manifolds" by Gromov (ProjetEuclid link), the author proves the following inequality (1.2) relating the systole and the filling radius of manifolds.
$$\...
- 469
9
votes
1
answer
281
views
Is every compact smooth Riemannian manifold bilipschitz equivalent to a finite simplicial complex?
Let $M$ be a compact smooth Riemannian manifold. Then it admits a triangulation, i.e. a finite simplicial complex $K$ which is homeomorphic to $M$. Any such simplicial complex carries a natural metric ...
- 91
8
votes
1
answer
358
views
Smoothing of piecewise Euclidean Riemannian metrics
Let $M$ be a smooth closed manifold and $T$ be a triangulation of $M$. Endow each simplex of $T$ with the Euclidean metric making it a regular simplex; this gives a piecewise Euclidean metric $g_0$ on ...
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