Helfrich’s energy and constrained minimisation
Helfrich’s energy and constrained minimisation
For every $g\in\mathbb{N}_0$ and $\epsilon>0$, we construct a smooth genus $g$ surface embedded into the unit ball with area $8\pi$ and Willmore energy smaller than $8\pi + \epsilon$. From this we deduce that a minimising sequence for Willmore's energy in the class of genus $g$ surfaces embedded in the unit …