A converse to Maz'ya's inequality for capacities under curvature lower bound
| dc.creator | Milman, Emanuel | |
| dc.date | 2009-03-27 | |
| dc.date.accessioned | 2026-07-07T12:57:32Z | |
| dc.date.available | 2026-07-07T12:57:32Z | |
| dc.description | We survey some classical inequalities due to Maz'ya relating isocapacitary inequalities with their functional and isoperimetric counterparts in a measure-metric space setting, and extend Maz'ya's lower bound for the $q$-capacity ($q>1$) in terms of the 1-capacity (or isoperimetric) profile. We then proceed to describe results by Buser, Bakry, Ledoux and most recently by the author, which show that under suitable convexity assumptions on the measure-metric space, Maz'ya's inequality for capacities may be reversed, up to dimension independent numerical constants: a matching lower bound on 1-capacity may be derived in terms of the $q$-capacity profile. We extend these results to handle arbitrary $q > 1$ and weak semi-convexity assumptions, by obtaining some new delicate semi-group estimates. | |
| dc.description | 26 pages, to appear in Springer's International Mathematical Series Vols. 10-13 | |
| dc.identifier | https://arxiv.org/abs/0903.4822 | |
| dc.identifier | http://arxiv.org/abs/0903.4822 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224963 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.title | A converse to Maz'ya's inequality for capacities under curvature lower bound | |
| dc.type | text |