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Geometric Analysis Seminar

Capillary and Free boundary embedded geodesics on Riemannian 2-disks with a strictly convex boundary

Dongyeong Ko

Location:  Hill-705
Date & time: Tuesday, 10 October 2023 at 2:50PM - 3:50PM

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. Finally, I will explain the Morse Index bound of such geodesics.

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