Let us imagine a water drop in space without the effect of gravity. If the drop is undisturbed it is spherical due to so called isoperimetric inequality. When we apply a small stress to the drop, it starts to wobble rather wildly and may even disintegrate into several smaller drops. This hints that the mathematical formulation of the motion of water drop is complicated. This is indeed true and it is mostly due to the fact the equations of motion may develop singularities such as disintegration in finite time, which is typical phenomenon for all geometric evolution equations. This project focuses on such equations and studies the questions of well-posedness, regularity and how the singularities develop.

2022

2026