# Mean Curvature Flow with Boundary

## TL;DR

This paper develops a comprehensive theory for surfaces with boundary evolving under mean curvature flow, establishing existence and boundary regularity results with minimal assumptions.

## Contribution

It introduces a general existence theorem via elliptic regularization and proves boundary regularity for surfaces with boundary under mild conditions.

## Key findings

- Proved existence of mean curvature flow with boundary.
- Established boundary regularity at all positive times.
- Used elliptic regularization technique.

## Abstract

We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under very mild hypotheses.