论文标题
曲率浓度较小的歧管
Manifolds with small curvature concentration
论文作者
论文摘要
在这项工作中，我们构造了像曲线浓度较小的歧管上有整体黑森结合的距离函数，并使用它来构建可能无限曲率的歧管上的ricci流动。作为一种应用，我们研究了这些流形的几何结构，而没有有限的曲率假设。特别是，我们表明具有RICCI下限，非阴性标态曲率，有界熵的歧管，Ahlfors $ n $ regular和小曲率浓度在拓扑上是欧几里得。
In this work, we construct distance like functions with integral hessian bound on manifolds with small curvature concentration and use it to construct Ricci flows on manifolds with possibly unbounded curvature. As an application, we study the geometric structure of those manifolds without bounded curvature assumption. In particular, we show that manifolds with Ricci lower bound, non-negative scalar curvature, bounded entropy, Ahlfors $n$-regular and small curvature concentration are topologically Euclidean.
