Variational convergence over metric spaces
| dc.creator | Kuwae, Kazuhiro | |
| dc.creator | Shioya, Takashi | |
| dc.date | 2005-05-20 | |
| dc.date.accessioned | 2026-07-07T05:20:05Z | |
| dc.date.available | 2026-07-07T05:20:05Z | |
| dc.description | We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a Gromov-Hausdorff convergent sequence. With the $L^p$-convergence, we establish a theory of variational convergences. We prove that the Poincaré inequality with some additional condition implies the asymptotic compactness. The asymptotic compactness is equivalent to the Gromov-Hausdorff compactness of the energy-sublevel sets. Supposing that the targets are $\CAT(0)$-spaces, we study convergence of resolvents. As applications, we investigate the approximating energy functional over a measured metric space and convergence of energy functionals with a lower bound of Ricci curvature. | |
| dc.identifier | https://arxiv.org/abs/math/0505430 | |
| dc.identifier | http://arxiv.org/abs/math/0505430 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75252 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C23; 49J45; 58E20 | |
| dc.title | Variational convergence over metric spaces | |
| dc.type | text |