  We study the modification of micromagnetic configurations in nanostructures,
due to the Dzyaloshinskii-Moriya interaction (DMI) that appear at the interface
of an ultrathin film. We show that this interaction leads to new micromagnetic
boundary conditions that bend the magnetization at the edges. We explore
several cases of ultrathin film nanostructures that allow analytical
calculations (1D systems, domain walls, cycloids and skyrmions), compare with
fully numerical calculations, and show that a good physical understanding of
this new type of micromagnetics can be reached. We particularly focus on
skyrmions confined in circular nanodots and show that edges allow for the
isolation of single skyrmions for a large range of the DMI parameter.
