# Non-spherical equilibrium shapes in the liquid drop model

## TL;DR

This paper proves the existence of non-spherical equilibrium shapes in the liquid drop model, showing bifurcation from spherical shapes and stability exchange.

## Contribution

It introduces a new family of volume-constrained critical points that are cylindrically symmetric but not spherical, expanding understanding of equilibrium shapes.

## Key findings

- Existence of non-spherical critical points bifurcating from the sphere
- Cylindrical symmetry of new solutions
- Stability exchange between spherical and non-spherical shapes

## Abstract

We prove the existence of a family of volume-constrained critical points of the liquid drop functional, which are cylindrically but not spherically symmetric. This family bifurcates from the ball and exchanges stability with it.