Student Geometry

I will talk about singularities of special Lagrangian surfaces.

Abstract: We overview classical results and open problems concerning minimal surfaces in Euclidian Space.

Given a smoothly bounded domain in three dimensions, we may consider the curl operator acting on divergence free vector fields tangent to the domain's boundary. It turns out that one only needs to impose a finite-dimensional set of additional boundary conditions to obtain a self-adjoint operator…

Abstract: We introduce a method of constructing (generalized) capillary surfaces via Gromov's "$\mu$-bubble" method. Using this, we study low-dimensional manifolds with nonnegative scalar curvature and strictly mean convex boundary. We prove a fill-in question of Gromov, a band-width estimate,…