Speaker: Dongyeong Ko (Rutgers)

Title: Capillary and free Boundary embedded geodesics on Riemannian 2-disks with a strictly convex boundary.

Abstract: The existence of embedded geodesics on surfaces is the foundational problem. I will explain the existence of two capillary embedded geodesics on Riemannian 2-disks with a strictly convex boundary with a certain condition via multi-parameter min-max construction. I will then explain the existence of two free boundary embedded geodesics on Riemannian 2-disks with a strictly convex boundary by free boundary curve shortening flow on surfaces, which is a free boundary analog of Grayson's theorem in 1989. Finally, I will explain the Morse index bound of such geodesics.