标题： 渐近锥形Kähler-Ricci流的唯一性 显示英文标题

标题： Uniqueness of asymptotically conical Kähler-Ricci flow

摘要： 我们研究了具有锥形初始条件的Kähler-Ricci流的唯一性问题。 给定一个非紧流形上的完整梯度扩展Kähler-Ricci孤立子，其曲率衰减为二次，包括其导数，我们建立了一个完整的解，该解从无穷远处孤立子的切锥出现——作为一个Käh勒锥——必须与与孤立子相关的前向自相似Kähler-Ricci流一致，前提是满足某些条件。 具体来说，如果它的凯勒形式保持在孤立子自相似Kähler-Ricci流的同一个上同调类中，其全黎曼曲率算子对于每个固定的正时间都是有界的，其里奇曲率在上方由A/t有界，其数量曲率在下方由-A/t有界，并且它与孤立子度量具有相同的 Killing 向量场。 本文部分回答了Feldman-Ilmanen-Knopf论文中的一个问题，并推广了Conlon-Deruelle和Conlon-Deruelle-Sun的早期工作。 显示英文摘要

摘要： We study the uniqueness problem for the K\"ahler-Ricci flow with a conical initial condition. Given a complete gradient expanding K\"ahler-Ricci soliton on a non compact manifold with quadratic curvature decay, including its derivatives, we establish that any complete solution to the Kahler-Ricci flow emerging from the soliton's tangent cone at infinity--appearing as a K\"ahler cone--must coincide with the forward self-similar K\"ahler-Ricci flow associated with the soliton, provided certain conditions hold. Specifically, if its K\"ahler form remains in the same cohomology class as that of the soliton's self-similar K\"ahler-Ricci flow, its full Riemann curvature operator is bounded for each fixed positive time, its Ricci curvature is bounded from above by A/t, its scalar curvature is bounded from below by -A/t, and it shares a same Killing vector field with the soliton metric. This paper gives a partial answer to a question in paper of Feldman-Ilmanen-Knopf, and generalizes the earlier work of Conlon-Deruelle and the work of Conlon-Deruelle-Sun.