Timeline for The continuity of Injectivity radius
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 29 at 10:55 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Math Jaxed
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| Jun 28, 2019 at 21:53 | comment | added | Nicolas Boumal | It is known that if M is connected and complete, then inj is a continuous function: see for example [Lee, Introduction to Riemannian Manifolds, 2018, Prop. 10.37]. See also this related question: mathoverflow.net/questions/335032/…. | |
| Jan 27, 2011 at 16:20 | vote | accept | Chih-Wei Chen | ||
| Jan 27, 2011 at 16:19 | comment | added | Chih-Wei Chen | Thank you a lot!! I should ask the question earlier, it had troubled me for one month... | |
| Jan 26, 2011 at 19:40 | answer | added | Anton Petrunin | timeline score: 17 | |
| Jan 26, 2011 at 19:16 | comment | added | Willie Wong | In fact, on any compact region of a smooth Riemannian manifold, you have that the injectivity radius is bounded below by a strictly positive number... (see the same reference that I gave above) | |
| Jan 26, 2011 at 19:03 | comment | added | Anton Petrunin | You write: "Inj(x) decreases to zero when x moves to the most curved point on a paraboloid." this is not true, InjRad does not not go to zero... | |
| Jan 26, 2011 at 19:01 | comment | added | Willie Wong | Are you sure about your paraboloid example? Take a look at Proposition 2.1.10 on Page 131 of W. Klingenberg's book Riemannian Geometry | |
| Jan 26, 2011 at 18:39 | history | edited | Chih-Wei Chen |
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| Jan 26, 2011 at 18:25 | history | asked | Chih-Wei Chen | CC BY-SA 2.5 |