Ricci Flow and Volume Renormalizability
With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra condition, then it is possible to define its renormalized volum...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210238 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Ricci Flow and Volume Renormalizability / E. Bahuaud, R. Mazzeo, E. Woolgar // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862743443735838720 |
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| author | Bahuaud, E. Mazzeo, R. Woolgar, E. |
| author_facet | Bahuaud, E. Mazzeo, R. Woolgar, E. |
| citation_txt | Ricci Flow and Volume Renormalizability / E. Bahuaud, R. Mazzeo, E. Woolgar // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra condition, then it is possible to define its renormalized volume and show that it is independent of choices that preserve this evenness structure. We prove that such expansions are preserved under normalized Ricci flow. We also study the variation of curvature functionals in this setting, and as one application, obtain the variation formula d/dtRenV(Mⁿ,g(t)) = −R∫Mⁿ(S(g(t)) + n(n−1))dVg(t), where S(g(t)) is the scalar curvature for the evolving metric g(t), and R∫(⋅)dVg is Riesz renormalization. This extends our earlier work to a broader class of metrics.
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| first_indexed | 2025-12-07T21:24:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210238 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:52Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bahuaud, E. Mazzeo, R. Woolgar, E. 2025-12-04T13:07:50Z 2019 Ricci Flow and Volume Renormalizability / E. Bahuaud, R. Mazzeo, E. Woolgar // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C44 arXiv: 1607.08558 https://nasplib.isofts.kiev.ua/handle/123456789/210238 https://doi.org/10.3842/SIGMA.2019.057 With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra condition, then it is possible to define its renormalized volume and show that it is independent of choices that preserve this evenness structure. We prove that such expansions are preserved under normalized Ricci flow. We also study the variation of curvature functionals in this setting, and as one application, obtain the variation formula d/dtRenV(Mⁿ,g(t)) = −R∫Mⁿ(S(g(t)) + n(n−1))dVg(t), where S(g(t)) is the scalar curvature for the evolving metric g(t), and R∫(⋅)dVg is Riesz renormalization. This extends our earlier work to a broader class of metrics. EB and RM are grateful to Robin Graham for discussions related to this work. The work of EB was supported by a Simons Foundation grant (#426628, E. Bahuaud). The work of EW was supported by an NSERC Discovery Grant RGPIN 203614. RM was supported by the NSF grants DMS-1105050 and DMS-1608223. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ricci Flow and Volume Renormalizability Article published earlier |
| spellingShingle | Ricci Flow and Volume Renormalizability Bahuaud, E. Mazzeo, R. Woolgar, E. |
| title | Ricci Flow and Volume Renormalizability |
| title_full | Ricci Flow and Volume Renormalizability |
| title_fullStr | Ricci Flow and Volume Renormalizability |
| title_full_unstemmed | Ricci Flow and Volume Renormalizability |
| title_short | Ricci Flow and Volume Renormalizability |
| title_sort | ricci flow and volume renormalizability |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210238 |
| work_keys_str_mv | AT bahuaude ricciflowandvolumerenormalizability AT mazzeor ricciflowandvolumerenormalizability AT woolgare ricciflowandvolumerenormalizability |