Minimal sets and cones in dimensions 3 and 4
Guy David, Université Paris Sud, Orsay, Francia. (pdf)
Viernes 19 de febrero de 2010 a las 11:30 en la sala 520 del módulo 17 de Ciencias, UAM
Resumen: Since Jean Taylor's work, the local structure of the two-dimensional minimal
(or almost minimal) sets (think about soap films in 3-space is well known; they are
locally equivalent, through C1 diffeomorphisms, to a minimal cone.
And there are exactly three types of minimal cones, which you can easily be observed in soap films.
In ambient dimension 4, the list of 2-dimensional minimal cones is not known yet,
and for instance the fact that the almost orthogonal union of two 2-planes is minimal
was only proved recently. This result will also be used as an excuse to discuss local
regularity properties of two-dimensional almost minimal sets in large ambient dimensions.