Timeline for Is the injectivity radius (semi) continuous on a non-complete Riemannian manifold?
Current License: CC BY-SA 4.0
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| Jul 12, 2019 at 20:55 | comment | added | Nicolas Boumal | Thanks Jack! I had a close look at your proof, and I believe I agree with every step. The more technical step (where you build a complete metric $\hat g$ on $\mathbb{R}^n$, smoothly transitioning from $g$ to the Euclidean metric) seems to be essentially the same as in Stephen's proof, where he does so by building a metric on a sphere, necessarily complete by compactness. Combining your two proofs should give continuity of $i(x)$ for any (connected) manifold, which is great. It looks like there should be a good way to write both of your arguments with the same language. | |
| Jul 9, 2019 at 23:14 | history | answered | Jack Lee | CC BY-SA 4.0 |