# Seminars & Colloquia Calendar

Geometric Analysis Seminar

## Planarity Estimate for the Mean Curvature Flow of Pinched Submanifolds in Higher Codimension

#### Keaton Naff (Columbia University)

Location:  via Zoom, https://rutgers.zoom.us/j/93880280324
Date & time: Tuesday, 29 September 2020 at 2:50PM - 3:50PM

Abstract: We will discuss the mean curvature flow of $$n$$-dimensional submanifolds of $$\mathbb{R}^{n+k}$$ satisfying a pinching condition introduced by Andrews and Baker, $$|H| > 0$$ and $$|A|^2 \leq c|H|^2$$. We will investigate how singularity formation in such flows resembles singularity formation in convex and two-convex flows in codimension one, established in the fundamental works of Huisken (1984) and Huisken-Sinestrari (2009). We will then discuss a quantitative estimate for this behavior.