LDR | | 00000nam u2200205 4500 |
001 | | 000000434399 |
005 | | 20200226150348 |
008 | | 200131s2019 ||||||||||||||||| ||eng d |
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▼a 9781392585627 |
035 | |
▼a (MiAaPQ)AAI22620071 |
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▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
082 | 0 |
▼a 510 |
100 | 1 |
▼a Appleton, Alexander J. |
245 | 10 |
▼a Singularities in U(2)-Invariant 4d Ricci Flow. |
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▼a [S.l.]:
▼b University of California, Berkeley.,
▼c 2019. |
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▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
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▼a 178 p. |
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▼a Source: Dissertations Abstracts International, Volume: 81-06, Section: B. |
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▼a Advisor: Bamler, Richard |
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▼a Thesis (Ph.D.)--University of California, Berkeley, 2019. |
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▼a This item must not be sold to any third party vendors. |
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▼a Firstly, we analyze the steady Ricci soliton equation for a certain class of metrics on complex line bundles over K\\"ahler-Einstein manifolds of positive scalar curvature. We show that these spaces admit a non-collapsed steady gradient Ricci soliton metric. In the four (real-) dimensional case, this yields a new family of non-collapsed steady Ricci solitons on the complex line bundles $O(-k)$, $k \\geq 3$, over $\\mathbb{C}P. |
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▼a 1$. These solitons are $U(2)$-invariant, non-K\\"ahler, and asymptotic to the the quotient of the four dimensional Bryant soliton by $\\Z_k$. As a byproduct of our work we also find Taub-Nut like Ricci solitons on $\\R. |
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▼a 4$ and demonstrate a new proof for the existence of the Bryant soliton.Secondly, we investigate the formation of singularities in four dimensional $U(2)$-invariant Ricci flow and show that the Eguchi-Hanson space can occur as a blow-up limit. In particular, we prove that starting from a class of asymptotically cylindrical $U(2)$-invariant initial metrics on $TS. |
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▼a 2$, a Type II singularity modeled on the Eguchi-Hanson space develops in finite time and the only possible blow-up limits are (i) the Eguchi-Hanson space, (ii) the flat $\\R. |
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▼a 4 / \\Z_2$ orbifold, (iii) the 4d Bryant soliton quotiented by $\\Z_2$, and (iv) the shrinking cylinder $\\R \imes \\R P. |
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▼a 3$. It also follows from our work that in four dimensional Ricci flow an embedded two dimensional sphere of any self-intersection number $k \\in \\Z$ may collapse to a point in finite time and thereby produce a singularity. For $|k|\\geq 3$ the singularities we construct are of Type II, yielding a new infinite family of Type II singularities. Numerical simulations indicate that their blow-up limits are the four dimensional steady Ricci solitons described above. |
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▼a School code: 0028. |
650 | 4 |
▼a Mathematics. |
690 | |
▼a 0405 |
710 | 20 |
▼a University of California, Berkeley.
▼b Mathematics. |
773 | 0 |
▼t Dissertations Abstracts International
▼g 81-06B. |
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▼t Dissertation Abstract International |
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▼a 0028 |
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▼a Ph.D. |
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▼a 2019 |
793 | |
▼a English |
856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15493683
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
980 | |
▼a 202002
▼f 2020 |
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▼a ***1008102 |
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▼a E-BOOK |