Nicolaos Kapouleas

In the first part of the talk (introduction) I will recall classical and semi-classical results and conjectures. In the second part I will review the current status of PDE gluing constructions of minimal surfaces. In the last (main) part of the talk...

I will first discuss doubling and desingularization constructions for minimal surfaces and applications on closed minimal surfaces in the round spheres, free boundary minimal surfaces in the unit ball, and self-shrinkers for the Mean Curvature flow...