Timeline for For proper group action on closed Riemannian manifold, must the union of orbits with non-unique closest points to a given point be of 0 volume measure

Current License: CC BY-SA 4.0

11 events

when toggle format	what		by	license	comment
Apr 20 at 12:31	history	edited	Learning math	CC BY-SA 4.0	added 8 characters in body
Apr 20 at 12:01	history	edited	Learning math	CC BY-SA 4.0	added 8 characters in body
Apr 16 at 18:48	history	edited	Michael Hardy	CC BY-SA 4.0	added 15 characters in body
Apr 16 at 2:12	answer	added	Saúl RM		timeline score: 2
Apr 16 at 1:35	comment	added	Saúl RM		It seems a statement similar to the question you asked earlier should be enough to prove that for almost all $p^$ in $M$, your condition holds (this is equivalent by Fubini to saying that for almost all $p\in M$, the set of points $p^$ for which $d(p^*,\cdot)$ is minimized at more than one point in $O_p$ has measure $0$)
Apr 16 at 1:24	comment	added	Learning math		@SaúlRM Thanks for confirming - okay let me think about it; my feeling is that for 'most' such $p^{*}\in M,$ it should be true - however, I'll sit down and think more...
Apr 16 at 1:22	comment	added	Saúl RM		Yes, I would choose one of the two intersections of the axis with $\mathbb{S}^2$
Apr 16 at 1:12	comment	added	Learning math		@SaúlRM Apologies, but the axis of rotation doesn't intersect the manifold $S^2$ except for the two end points, right? So does this mean you're choosing one of these two end points? P.S. I may reply in a few hours, since it's very late where I'm writing this from.
Apr 16 at 1:03	comment	added	Saúl RM		Wouldn't this be not hold when $\mathbb{S}^1$ acts on $\mathbb{S}^2$ by rotations around some fixed axis, and if you let $p^*$ be a point in that axis?
Apr 16 at 0:49	history	edited	Learning math	CC BY-SA 4.0	added 110 characters in body
Apr 16 at 0:43	history	asked	Learning math	CC BY-SA 4.0