31 oct 2012 -- 17:00
Sala Seminari, Department of Mathematics, Pisa University
We consider the class of timelike minimal surfaces in the flat Minkowski space, which admit a $C^1$ parametrization of a specic form. We prove that, if the distinguished parametrization is in fact $C^k$, then the surface is regularly immersed away from a singular set of dimension at most $1+1/k$, and that this bound is sharp. We also show that, generically with respect to a natural topology, if $n=2$ the singular set is one-dimensional, and if $n\ge$ 4 the singular set is empty. For $n=3$ both situations can occurr.