Instantaneous convexity breaking for the quasi-static droplet model

TL;DR

This paper demonstrates that in a quasi-static droplet model, the convex shape of a liquid droplet can be instantly lost, challenging assumptions about shape stability over time.

Contribution

It provides a specific example showing that convexity can be broken instantaneously in a well-known quasi-static droplet model.

Findings

Convexity of the droplet domain can be instantaneously broken.

The model exhibits non-preservation of convexity over time.

Shape evolution can include sudden loss of convexity.

Abstract

We consider a well-known quasi-static model for the shape of a liquid droplet. The solution can be described in terms of time-evolving domains in $\mathbb{R}^n$. We give an example to show that convexity of the domain can be instantaneously broken.