Timeline for Is this $a(p)=\lim_{r\to \infty} \frac{VolS(p,r)}{e^{h r}}$ exists and applied for manifolds with positive curvature?

13 events

when toggle format	what		by	license	comment
Apr 17, 2020 at 12:35	vote	accept	zeraoulia rafik
Apr 12, 2020 at 19:54	answer	added	freidtchy		timeline score: 1
Apr 12, 2020 at 16:48	answer	added	Ben McKay		timeline score: 0
Apr 12, 2020 at 16:45	comment	added	Sebastian Goette		@BenMcKay Surely you mean the Bishop-Gromov comparison theorem? The denominator usually is the analogous volume in a comparison space. So I believe that the denominator $e^{hr}$ will produce less significant results ($0$ whenever $\operatorname{Ric}\ge 0$ if I am not mistaken). And am I right that $r$ is not meant to be constant?
Apr 12, 2020 at 16:40	comment	added	Ben McKay		I think volume of balls is governed by Ricci, so should be no problem. Try Gromov, Sign and geometric meaning of curvature.
Apr 12, 2020 at 16:08	history	edited	zeraoulia rafik	CC BY-SA 4.0	added 141 characters in body
Apr 12, 2020 at 15:06	history	edited	zeraoulia rafik	CC BY-SA 4.0	deleted 9 characters in body
Apr 12, 2020 at 14:55	history	edited	zeraoulia rafik	CC BY-SA 4.0	added 7 characters in body; edited title
Apr 12, 2020 at 14:50	history	edited	zeraoulia rafik	CC BY-SA 4.0	added 7 characters in body; edited title
Apr 12, 2020 at 14:45	comment	added	zeraoulia rafik		I meant Volume of spheres
Apr 12, 2020 at 14:45	history	edited	zeraoulia rafik	CC BY-SA 4.0	added 7 characters in body; edited title
Apr 12, 2020 at 14:43	comment	added	Ben McKay		What is $S(p,r)$? What is $\operatorname{exp}(hr)$?
Apr 12, 2020 at 14:38	history	asked	zeraoulia rafik	CC BY-SA 4.0