Some Progress in Conformal Geometry
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147215 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862542318332018688 |
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| author | Sun-Yung A. Chang Qing, J. Yang, P. |
| author_facet | Sun-Yung A. Chang Qing, J. Yang, P. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-24T18:45:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147215 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T18:45:31Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sun-Yung A. Chang Qing, J. Yang, P. 2019-02-13T19:11:07Z 2019-02-13T19:11:07Z 2007 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 https://nasplib.isofts.kiev.ua/handle/123456789/147215 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. This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Some Progress in Conformal Geometry Article published earlier |
| spellingShingle | Some Progress in Conformal Geometry Sun-Yung A. Chang Qing, J. Yang, P. |
| title | Some Progress in Conformal Geometry |
| title_full | Some Progress in Conformal Geometry |
| title_fullStr | Some Progress in Conformal Geometry |
| title_full_unstemmed | Some Progress in Conformal Geometry |
| title_short | Some Progress in Conformal Geometry |
| title_sort | some progress in conformal geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147215 |
| work_keys_str_mv | AT sunyungachang someprogressinconformalgeometry AT qingj someprogressinconformalgeometry AT yangp someprogressinconformalgeometry |