On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves
On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves
For a smooth closed embedded planar curve $\Gamma$, we consider the minimization problem of the Willmore energy among immersed surfaces of a given genus $\mathfrak{g}\geq1$ having the curve $\Gamma$ as boundary, without any prescription on the conormal. By general lower bound estimates, in case $\Gamma$ is a circle we prove …