论文标题
关于有限的时间类型的I奇点，Kähler-Ricci流在紧凑的Kähler表面上
On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces
论文作者
论文摘要
我们表明，完整的非压缩两件界限尺寸缩小的梯度Kähler-ricci soliton $（m，\，\，g，\，x）$与soliton $ g $与有限的标量曲率$ \ perperatornAme {r} $ culit culit at $ cure x cultector ant sol culit cultector ant Solitys unting usity ant solitys unity，culit culit cur x culit ant $ \ operatoTorname {r} _ {g} \ not \ to0 $是biholomorphic to $ \ mathbb {c} \ times \ times \ mathbb {p}^{1} $，或者对此一度的爆炸。假设在后一种歧管上存在这样的孤子，我们表明它是感谢您的和独特的。我们还标识相应的孤子矢量场。鉴于这些可能性，然后我们证明了Feldman-Ilmanen-Knopf的强烈形式，即在紧凑的Kähler表面上对Kähler-Ricci流的有限时间I奇异性，从而导致了此维度中这种奇异性的气泡的分类。
We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient Kähler-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 Kähler-Ricci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension.
