# Singularity formation in axially symmetric mean curvature flow with Neumann boundary

## TL;DR

This paper investigates the behavior of axially symmetric surfaces evolving under mean curvature flow with Neumann boundary conditions, demonstrating that any initial singularity occurring is necessarily of type I.

## Contribution

It establishes that all first singularities in such flows are of type I, providing a classification of singularity types under these boundary conditions.

## Key findings

- All first singularities are of type I.
- The analysis applies to smooth, axially symmetric surfaces.
- Results contribute to understanding singularity formation in geometric flows.

## Abstract

We study mean curvature flow of smooth, axially symmetric surfaces in $\mathbb{R}^3$ with Neumann boundary data. We show that all singularities at the first singular time must be of type I.