Is there a solution or progress of the following problem (maybe old conjecture): Is An immersed surface with constant mean curvature and with a circle as a boundary part of a sphere??. If we replace "immersed" by "embedded" I think the problem was solved by Alexandroff kind of long time ago. Is someone could enlighten about what exactly Alexandroff solves and what is to do, it would help me a lot.


Thanks
Mario



Immersed surface with circle as a boundary
Check out [this paper of Rafael Lopez](http://www.ugr.es/~rcamino/publications/pdf/art14.pdf) and references therein.


