# A planarity estimate for pinched solutions of mean curvature flow

## TL;DR

This paper proves that certain pinched solutions to mean curvature flow in Euclidean space, when blown up, are necessarily of codimension one, advancing understanding of the geometric structure of these solutions.

## Contribution

It establishes that blow-ups of compact pinched mean curvature flow solutions are necessarily codimension one, under specific initial conditions.

## Key findings

- Blow-ups of pinched solutions are codimension one.
- Pinching condition constrains the geometric complexity.
- Results apply to compact solutions in Euclidean space.

## Abstract

We show that the blow-ups of compact solutions to the mean curvature flow in $\mathbb{R}^N$ initially satisfying the pinching condition $|A|^2 < c |H|^2$ for a suitable constant $c = c(n)$ must be codimension one.