On the existence of degenerate solutions of the two-dimensional $H$-system

André Guerra, Xavier Lamy, Konstantinos Zemas

We consider entire solutions $\omega \in {\dot{H}}^1({\mathbb{R}}^2;{\mathbb{R}}^3)$ of the $H$-system $\Delta \omega =2{\omega }_x\wedge {\omega }_y,$ which we refer to as bubbles. Surprisingly, and contrary to conjectures r…