Timeline for On the Lipschitz continuity of the unit-normal vector field of a polytope

9 events

when toggle format	what		by	license	comment
Dec 28, 2021 at 15:51	vote	accept	dohmatob
Dec 28, 2021 at 15:44	answer	added	Dustin G. Mixon		timeline score: 1
Dec 28, 2021 at 15:31	history	edited	dohmatob	CC BY-SA 4.0	added 1 character in body
Dec 28, 2021 at 15:01	history	edited	dohmatob	CC BY-SA 4.0	added 28 characters in body
Dec 28, 2021 at 15:00	comment	added	dohmatob		Indeed. I forgot to mention that I only care about the condition holding on arbitrarily small neighborhood of $P$. In particular, the low-dim faces of the polytope form a set of measure zero. Thus we can always construct an arbitrarily small neighborhood of $P$ and work on it instead.
Dec 28, 2021 at 14:56	history	edited	dohmatob	CC BY-SA 4.0	added 132 characters in body
Dec 28, 2021 at 14:41	comment	added	Dustin G. Mixon		If $P=\{0\}$, then $u(x)=x/\\|x\\|$, which is not Lipschitz near $P$. Similar behavior occurs in general near lower-dimensional faces of a polytope.
Dec 28, 2021 at 11:50	history	edited	dohmatob		edited tags
Dec 28, 2021 at 11:38	history	asked	dohmatob	CC BY-SA 4.0