Timeline for Homotopy bounds in simply connected complete Riemannian manifolds
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2015 at 11:40 | vote | accept | Jesús Álvarez | ||
| Mar 6, 2015 at 11:19 | answer | added | John Harvey | timeline score: 2 | |
| Mar 6, 2015 at 10:54 | comment | added | Jesús Álvarez | The following is a simpler variation of the above question: Does there exist a non-decreasing $R:\mathbb R_+\to\mathbb R_+$ such that, for every $r>0$ and all piecewise smooth paths $\alpha,\beta$ from $x$ to any $y\in B(x,r)$ with length $<r$, there is a homotopy relative to the end points between $\alpha$ and $\beta$ consisting of piecewise smooth paths of length $<R$? It seems that an affirmative answer to this question could be given by using convex balls $B(x_i,s_i)$ so that the centers $x_i$ form a discrete subset of $M$ and the balls $B(x_i,s_i/2)$ cover $M$. Is this known? | |
| Mar 6, 2015 at 9:50 | history | asked | Jesús Álvarez | CC BY-SA 3.0 |