发表机构
University of California Berkeley; Universitat de València（加州大学伯克利分校; 瓦伦西亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了Petrunin光滑化猜想：任意紧致无边界非负Alexandrov曲率的多面体空间是光滑黎曼轨形空间的Gromov-Hausdorff极限，通过新Ricci流短时间存在理论实现，并给出积分曲率缺陷的刚性应用。
AI 中文摘要
我们证明了Petrunin在所有维度上的光滑化猜想：每个紧致无边界的欧几里得多面体空间，若具有非负Alexandrov曲率，则是具有几何非负曲率的光滑黎曼轨形空间的Gromov-Hausdorff极限。更强地，逼近度量是单一轨形Ricci流的正时间切片，其度量初始条件为给定的多面体空间。证明依赖于Ricci流新的短时间存在性和正则化理论，在双侧体积界和广义线段不等式下，该理论将逐点下曲率控制替换为对来自保持曲率锥的缺陷的小尺度不变积分控制。尽管允许任意大的逐点违反，该理论产生的存在时间和正时间曲率估计独立于初始上曲率界。作为进一步应用，它为具有小积分曲率缺陷的流形提供了刚性结论。
英文摘要
We prove Petrunin's smoothing conjecture in all dimensions: every compact Euclidean polyhedral space without boundary and with nonnegative Alexandrov curvature is a Gromov-Hausdorff limit of smooth Riemannian orbifolds with geometrically nonnegative curvature. More strongly, the approximating metrics are positive-time slices of a single orbifold Ricci flow whose metric initial condition is the given polyhedral space. The proof rests on a new short-time existence and regularization theory for Ricci flow that, under two-sided volume bounds and a generalized segment inequality, replaces pointwise lower curvature control by small scale-invariant integral control of the defect from a preserved curvature cone. Although it allows arbitrarily large pointwise violations, this theory yields an existence time and positive-time curvature estimates independent of the initial upper curvature bound. As a further application, it gives rigidity consequences for manifolds with small integral curvature defect.
