Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Lynch, Stephen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215079884