2014/08/28 by Roberta Alessandroni, Alessandroni, Roberta, Ernst Kuwert +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG
paper · pdf · doi:10.48550/arxiv.1408.6670
arxiv created 2014/08/28 · arxiv updated 2014/08/29
We consider a free boundary problem for the Willmore functional. Given a smooth domain Ω in \mathbb R3, we construct Willmore disks wich are critical in the class of surfaces meeting ∂ Ω orthogonally along their boundary and having small prescribed area. Using rescaling we first obtain constrained solutions with prescribed two-dimensional barycenter, and then study the variation of the barycenter.