当前位置: X-MOL 学术Math. Z. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The Chern–Ricci flow on primary Hopf surfaces
Mathematische Zeitschrift ( IF 1.0 ) Pub Date : 2021-04-18 , DOI: 10.1007/s00209-021-02735-5
Gregory Edwards

The Hopf surfaces provide a family of minimal non-Kähler surfaces of class VII on which little is known about the Chern–Ricci flow. We use a construction of Gauduchon–Ornea for locally conformally Kähler metrics on primary Hopf surfaces of class 1 to study solutions of the Chern–Ricci flow. These solutions reach a volume collapsing singularity in finite time, and we show that the metric tensor satisfies a uniform upper bound, supporting the conjecture that the Gromov-Hausdorff limit is isometric to a round\(S^1\). Uniform \(C^{1+\beta }\) estimates are also established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.



中文翻译:

在Hopf主面上的Chern-Ricci流

Hopf曲面提供了最小的VII类非Kähler曲面族,在该曲面上对Chern-Ricci流的了解很少。我们使用Gauduchon-Ornea的构造对1类主要Hopf曲面上的局部保形Kähler度量进行研究,以研究Chern-Ricci流的解。这些解在有限时间内达到了体积崩溃的奇点,并且我们证明了度量张量满足一个统一的上限,这支持了Gromov-Hausdorff极限等距到圆\(S ^ 1 \)的猜想。还建立了潜力的统一\(C ^ {1+ \ beta} \)估计。以前的结果仅是关于Hopf表面的最简单示例才知道的。

更新日期:2021-04-18
down
wechat
bug