发表机构
School of Mathematics and Statistics, Northeast Normal University（东北师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在积分体积亏损界下证明非坍缩Ricci极限空间的度量奇异集余维数至少为四，并具有sigma有限测度，验证了余维四正则性猜想的一个特例，且该界是尖锐的。
AI 中文摘要
设$(X,d,p)$为$n$维非坍缩Ricci极限空间，其中$n\ge4$。在积分体积亏损界下，我们证明度量奇异集的Hausdorff余维数至少为四，且具有sigma有限的$(n-4)$维Hausdorff测度。这建立了余维四正则性猜想的一个特例。此外，非流形点集是闭的，且具有局部有限的$(n-4)$维Hausdorff测度，其与每个有界球的交集满足$r^4$阶的管状体积估计。在四维情形，非流形点构成局部有限集。一个平坦商空间例子表明余维数界是尖锐的。
英文摘要
Let $(X,d,p)$ be an $n$-dimensional noncollapsed Ricci limit space, where $n\ge4$. Under an integral volume-deficit bound, we prove that the metric singular set has Hausdorff codimension at least four and sigma-finite $(n-4)$-dimensional Hausdorff measure. This establishes a special case of the codimension-four regularity conjecture. Moreover, the nonmanifold locus is closed and has locally finite $(n-4)$-dimensional Hausdorff measure, and its intersection with each bounded ball satisfies a tubular-volume estimate of order $r^4$. In dimension four, the nonmanifold points form a locally finite set. A flat quotient example shows that the codimension bound is sharp.
