## Diff. Geom, Math. Phys., PDE Seminar: Leobardo Rosales

- Date: 05/13/2014
- Time: 11:00

*Korea Institute for Advanced Study (KIAS)*

University of British Columbia

The $c$-Plateau problem for surfaces in space

The c-Plateau problem for surfaces in space asks, given $c>0$ and $\gamma$ a closed curve in space, whether we can find $M_{c}$ a smooth orientable surface-with-boundary, with $\partial M_{c} = \sigma_{c}+\gamma$ where $\sigma_{c}$ is a finite union of closed curves disjoint from $\gamma,$ minimizing $c$-isoperimetric mass $\mathbf{M}^{c}(M) := \text{area}(M)+c \cdot \text{length}(\partial M)^{2}$ amongst all $M$ smooth orientable surfaces-with-boundary, with $\partial M = \sigma+\gamma$ where $\sigma$ is a finite union of closed curves disjoint from $\gamma$. In this talk we give several regularity results for solutions to the $c$-Plateau problem, formulated in the more general setting of integer two-rectifiable currents.

Location: ESB 4127