Timeline for Lipschitz Approximation to a PW Smooth Map
Current License: CC BY-SA 3.0
11 events
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| Aug 11, 2013 at 17:22 | answer | added | Vidit Nanda | timeline score: 1 | |
| Aug 11, 2013 at 5:23 | comment | added | Ryan Budney | You're welcome. It's helpful to think through some basic examples like this when contemplating these kinds of questions. | |
| Aug 11, 2013 at 5:13 | comment | added | Danny Brown | ...yep. Thanks. Sorry for such a silly question. | |
| Aug 11, 2013 at 4:57 | comment | added | Ryan Budney | If I understand your question correctly, let $f : \mathbb R \to \mathbb R$ be the absolute value function. It is piecewise smooth for some triangulation of $\mathbb R$, and smooth on any subcomplex not containing the origin. But any smooth approximation to $f$ can not be close to $f$ in the Lipschitz norm. You could construct a version of this for compact manifolds, replace $\mathbb R$ with $[-1,1]$ for example. Does this answer your question? | |
| Aug 11, 2013 at 4:53 | history | edited | Danny Brown | CC BY-SA 3.0 |
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| Aug 11, 2013 at 4:19 | comment | added | Danny Brown | @RyanBudney It does look like relative smooth approximation. I couldn't see how to add Lipschitz closeness to the proof though. | |
| Aug 11, 2013 at 1:28 | comment | added | Ryan Budney | gt is very appropriate. Have you tried Hirsch's textbook "Differential Topology"? This looks like the relative smooth approximation theorem. | |
| Aug 10, 2013 at 22:12 | history | edited | Danny Brown | CC BY-SA 3.0 |
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| Aug 9, 2013 at 23:31 | history | edited | Danny Brown | CC BY-SA 3.0 |
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| Aug 9, 2013 at 23:29 | review | First posts | |||
| Aug 9, 2013 at 23:35 | |||||
| Aug 9, 2013 at 23:10 | history | asked | Danny Brown | CC BY-SA 3.0 |