Capillary surfaces inside polyhedral regions
  In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is prescribed to be any value in $(\frac{\pi}{2}, \pi]$ and it is allowed to vary from one boundary component to the other. 
Antonio Alarcon and Rabah Souam
math.DG