论文标题
Ricci流的古老解决方案，具有I型曲率生长
Ancient solutions of Ricci flow with Type I curvature growth
论文作者
论文摘要
RICCI流的古老解决方案自然出现为奇异性形成的模型。在自然几何假设下，在这种溶液分类方面取得了重大进展。现在已经充分了解了尺寸2和3的非弯曲溶液，以及更高维度的PIC解。我们考虑了完整的任意维度的古老解决方案，具有类型的曲率生长。我们表明，$κ$ -Noncollapsed类型〜I古代解决方案，该解决方案是非恰当的，并且具有非负分段曲率必须至少分解一个欧几里得因素。因此，$κ$ -Noncollapsed类型〜I古代解决方案（弱pic2）是本地对称的空间。
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natural geometric assumptions. Nonnegatively curved solutions in dimensions 2 and 3, and uniformly PIC solutions in higher dimensions are now well understood. We consider ancient solutions of arbitrary dimension which are complete and have Type~I curvature growth. We show that a $κ$-noncollapsed Type~I ancient solution which is noncompact and has nonnegative sectional curvature necessarily splits at least one Euclidean factor. It follows that a $κ$-noncollapsed Type~I ancient solution which is weakly PIC2 is a locally symmetric space.
