Axially symmetric volume constrained anisotropic mean curvature flow

TL;DR

This paper investigates the long-term behavior of an anisotropic mean curvature flow for axially symmetric drops with free boundaries, establishing existence results and providing numerical simulations.

Contribution

It introduces a long-time existence theory for a non-local anisotropic mean curvature flow with free boundaries in axially symmetric settings.

Findings

Flow exists for all time for large volume initial surfaces.

Numerical simulations illustrate the curvature flow behavior.

The study extends understanding of anisotropic free boundary problems.

Abstract

We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume, we show that the flow exists for all time. Numerical simulations of the curvature flow are presented.