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Singularities in U(2)-Invariant 4d Ricci Flow
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Singularities in U(2)-Invariant 4d Ricci Flow. |
| 개인저자 | Appleton, Alexander J. |
| 단체저자명 | University of California, Berkeley. Mathematics. |
| 발행사항 | [S.l.]: University of California, Berkeley., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 178 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-06B. Dissertation Abstract International |
| ISBN | 9781392585627 |
| 학위논문주기 | Thesis (Ph.D.)--University of California, Berkeley, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-06, Section: B.
Advisor: Bamler, Richard |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | 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 $\\mathbb{C}P. |
| 요약 | 1$. 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 $\\R. |
| 요약 | 4$ 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 $TS. |
| 요약 | 2$, 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 $\\R. |
| 요약 | 4 / \\Z_2$ orbifold, (iii) the 4d Bryant soliton quotiented by $\\Z_2$, and (iv) the shrinking cylinder $\\R \imes \\R P. |
| 요약 | 3$. 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. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
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