Geometry Seminar: D. Wiygul (ETH)
Geometry Seminar (Geometric Analysis)
Speaker: David Wiygul (ETH)
Title: Uniqueness and Morse index of minimal surfaces in the sphere and ball
Abstract: I will present some recent work with Alessandro Carlotto and Mario Schulz that in some respects builds on and in other respects complements earlier work with Nicos Kapouleas, which I will also review. Specifically, I will review the result with Kapouleas that each of Lawson's embedded minimal surfaces in the 3-sphere is uniquely determined by its topological type and symmetry group, and I will review the calculation, also with Kapouleas, of the Morse index of an infinite subfamily of these same surfaces. Then, somewhat complementarily, I will describe the construction with Carlotto and Schulz of a family of free boundary minimal surfaces in the 3-ball having the same topological types and symmetries as those of a previously identified family, and I will further describe some index estimates for our new surfaces.