五维和六维中的平面性估计
The planarity estimate in dimensions five and six
- King’s College London（伦敦国王学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文填补了Naff平面性估计在5维和6维的空白，通过引入尖锐的Kato型不等式，在完整Andrews-Baker范围内证明了该估计。
AI中文摘要：
Naff的平面性估计是分析高余维二次夹挤平均曲率流奇点的重要工具，表明高曲率区域渐近地成为余维一。Naff在至少7维的整个Andrews-Baker夹挤范围内建立了该估计，而在5维和6维中则需要更强的夹挤假设。我们填补了这一剩余空白，证明了在5维和6维中整个Andrews-Baker范围内的平面性估计。关键的新工具是一个尖锐的Kato型不等式，将主法线的扭转与第二基本形式的梯度联系起来。
英文摘要：
Naff's planarity estimate is a crucial tool for analysing singularities of quadratically pinched mean curvature flows in high codimension, showing that high-curvature regions become asymptotically codimension one. Naff established the estimate throughout the full Andrews--Baker pinching range in dimensions at least $7$, while in dimensions $5$ and $6$ a stronger pinching assumption was required. We close this remaining gap, proving the planarity estimate in dimensions $5$ and $6$ throughout the full Andrews--Baker range. The key new ingredient is a sharp Kato-type inequality relating the twisting of the principal normal to the gradient of the second fundamental form.
