Singularities in flat multiply connected ferromagnet and Abel's theorem

Ferromagnetic films several nanometers thick are the prospective material for the next generation of microelectronic components. They realize the whole world, consisting of interacting magnetic vortices, which may be conveniently described in terms of theory of complex variables functions. David Gross introduced the class of so-called meronic solutions for the distribution of the magnetization in such materials. We will show that the locations of singularities for these solutions in multiply-connected domains are subjected to restrictions emerging from Abel's theorem. (Joint work with K. L. Metlov)