Timeline for Smoothness of Minkowski functional is equivalent to smoothness of boundary
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 4 at 6:27 | comment | added | HelloEveryone | Maybe a question concerning this matter: is the Minkowski functional $f_C(x)$ always differentiable on the set of points $\{x\in\mathbb{R}^n: f_c(x)>1\}$, i.e. in the points that are outside the set $C$? Intuitively this should be true, since a similar result also holds true for the distance function to some convex set $C$. Would be great if somebody has a reference! | |
| Apr 16, 2023 at 15:21 | comment | added | Smooth Alpert Frame | Yes, that seems reasonable to me. | |
| Apr 16, 2023 at 8:17 | comment | added | Alexander Schmeding | That is correct and was not mentioned in my answer. One should recheck the proof but from the top of my head it does not use the norm property in the step in an integral way. | |
| Apr 14, 2023 at 12:52 | comment | added | Smooth Alpert Frame | It's only a norm when the domain is balanced I think. | |
| Jan 7, 2022 at 17:47 | vote | accept | ABIM | ||
| Jan 7, 2022 at 17:32 | history | answered | Alexander Schmeding | CC BY-SA 4.0 |