发表机构
School of Science, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非紧复流形上瞬时完备Chern-Ricci流的强唯一性，在弱假设下建立初始度量的唯一性，并证明欧几里得度量下流的平稳性及复曲面Ricci流的Kähler性质保持。
AI 中文摘要
本文研究了非紧复流形上光滑瞬时完备Chern-Ricci流的强唯一性。在适当的参考度量和正性假设下，我们建立了在紧集外为Kähler的初始Hermitian度量的强唯一性。初始度量可以是不完备的，并且不对演化解施加曲率、度量比较或增长界。特别地，我们在此类中从具有有界Chern-Ricci曲率的完备初始度量获得强唯一性。我们还证明了从$\mathbb{C}^n$上的欧几里得度量出发的流的平稳性，以及从复单位球上的欧几里得度量出发的瞬时完备流在所有正时间上的唯一性。最后，在复曲面上，我们证明了若一个Ricci流在固定复结构下保持Hermitian，且在某时刻为Kähler，则它在所有时刻均为Kähler，并由此推导出此类Ricci流的相应强唯一性结果。
英文摘要
In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on $\mathbb{C}^n$ and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.
Comments21 pages, all comments welcome
