**22 mar 2019 - 24 mar 2019**

University of Hawaii Manoa

The aim of the proposed workshop is to gather both senior and junior mathematicians whose research has been devoted to the study of the regularity properties of the solutions of three geometric problems: the Plateau problem, the existence of minimal surfaces via Min-max constructions and the mean curvature flow. The Plateau problem consists in finding a surface with least area among all the surfaces spanning a prescribed boundary. Lack of compactness leads to the proof of existence results in weak spaces. The natural question is how singular the minimizers can be. In particular, we are interested in interior and boundary regularity theorems. More generally, one can consider critical points of the area functional in general Riemannian manifolds. In this case, existence can be proven using min-max techniques. Finally, we propose to dedicate some talks to the recent developments on the gradient flow of the area functional (and of more general anisotropic energies), called mean curvature flow. We hope that this meeting will foster exchange of ideas in these closely related subjects and will allow to establish new fruitful collaborations.