Free boundary minimal surfaces in the unit ball
speaker: Mario Schulz (WWU)abstract: Free boundary minimal surfaces arise naturally in partitioning problems for convex bodies and capillarity problems for fluids. The case of the Euclidean unit ball as ambient manifold for free boundary minimal surfaces is of particular interest for the study of extremal metrics for Steklov eigenvalues on surfaces with boundary. The theory has been developed in various interesting directions, yet many fundamental questions remain open. Two of the most basic ones can be phrased as follows: (1) Can a surface of any given topology be realised as an embedded free boundary minimal surface in the 3-dimensional Euclidean unit ball? We answer this question affirmatively for surfaces with connected boundary and arbitrary genus. (2) When they exist, are such embeddings unique up to ambient isometry? We answer this question in the strongest negative terms by providing pairs of non-isometric free boundary minimal surfaces with the same topology and symmetry group.
timetable:
Thu 15 Sep, 11:15 - 12:15, Aula Dini
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