Timeline for When minimum of two supporting functionals of convex bodies is convex?

10 events

when toggle format	what		by	license	comment
S Jun 19, 2017 at 9:30	history	suggested	Martin Sleziak	CC BY-SA 3.0	MathJax: \langle, \rangle
Jun 19, 2017 at 9:02	review	Suggested edits
S Jun 19, 2017 at 9:30
Jun 19, 2017 at 7:26	vote	accept	asv
Jun 19, 2017 at 6:31	answer	added	Fedor Petrov		timeline score: 10
Jun 19, 2017 at 5:47	comment	added	asv		@IvanIzmestiev : I still think the post is correct. You are right that $\max\{h_A,h_B\}$ is always convex. But the point is that if the union of the sets is convex then $\min\{h_A,h_B\}$ is also convex because it is equal to the supporting functional $h_{A\cap B}$ of the intersection.
Jun 18, 2017 at 20:09	comment	added	Ivan Izmestiev		It seems to me that one should take maximum instead of minimum. (The supremum of union of two sets is the maximum of two suprema.) The maximum of two convex functions is always convex, and the maximum of two support functions is the support function of the convex envelope of the union. By the way, the support function of the intersection has quite a complicated description, see Remark 3 to Chapter 1.8 of Schneider's "Brunn-Minkowski theory".
Jun 18, 2017 at 18:47	comment	added	asv		@ChristianRemling No, I did not mix them up. I did not find an answer to my question in your link.
Jun 18, 2017 at 16:09	history	edited	asv	CC BY-SA 3.0	edited title
Jun 18, 2017 at 14:52	history	edited	asv	CC BY-SA 3.0	deleted 1 character in body
Jun 18, 2017 at 14:09	history	asked	asv	CC BY-SA 3.0