Some Progress in Conformal Geometry
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Some Progress in Conformal Geometry
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| Creator |
Sun-Yung A. Chang
Qing, J. Yang, P. |
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| 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 σ2-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.
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| Date |
2019-02-13T19:11:07Z
2019-02-13T19:11:07Z 2007 |
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| Type |
Article
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| Identifier |
Some Progress in Conformal Geometry / Sun-Yung A. Chang, J. Qing, P. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 53A30; 53C20; 35J60 http://dspace.nbuv.gov.ua/handle/123456789/147215 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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