Some Progress in Conformal Geometry
| dc.creator | Chang, Sun-Yung A. | |
| dc.creator | Qing, Jie | |
| dc.creator | Yang, Paul | |
| dc.date | 2007-12-17 | |
| dc.date.accessioned | 2026-07-07T09:34:50Z | |
| dc.date.available | 2026-07-07T09:34:50Z | |
| dc.description | This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $σ_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes. | |
| dc.description | This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0712.2794 | |
| dc.identifier | http://arxiv.org/abs/0712.2794 | |
| dc.identifier | SIGMA 3 (2007), 122, 17 pages | |
| dc.identifier | doi:10.3842/SIGMA.2007.122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159636 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Some Progress in Conformal Geometry | |
| dc.type | text |