تقرير
On finite time Type I singularities of the K\'ahler-Ricci flow on compact K\'ahler surfaces
| العنوان: | On finite time Type I singularities of the K\'ahler-Ricci flow on compact K\'ahler surfaces |
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| المؤلفون: | Cifarelli, Charles, Conlon, Ronan J., Deruelle, Alix |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry |
| الوصف: | We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient K\"ahler-Ricci soliton $(M,\,g,\,X)$ with soliton metric $g$ with bounded scalar curvature $\operatorname{R}_{g}$ whose soliton vector field $X$ has an integral curve along which $\operatorname{R}_{g}\not\to0$ is biholomorphic to either $\mathbb{C}\times\mathbb{P}^{1}$ or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the Feldman-Ilmanen-Knopf conjecture for finite time Type I singularities of the K\"ahler-Ricci flow on compact K\"ahler surfaces, leading to a classification of the bubbles of such singularities in this dimension. Comment: 32 pages; oversight in the proof of Theorem B rectified (uniform lower bound on volume of curves) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.04380 |
| رقم الأكسشن: | edsarx.2203.04380 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |