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Relating the index and the topology of (free boundary) minimal surfaces

Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis August 21, 2024 - August 23, 2024

August 23, 2024 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Giada Franz (Massachusetts Institute of Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Relating the index and the topology of (free boundary) minimal surfaces

Abstract

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In this talk, I will discuss existing results and open problems about estimating the Morse index of a (free boundary) minimal surface from below by a function of its topology.
I will mostly focus on results proving that the Morse index of a free boundary minimal surface in a three-dimensional Riemannian manifold grows linearly with the product of its area and its topology. This is joint work with Santiago Cordero-Misteli, and it is inspired by Antoine Song's result in the closed case.

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Relating the index and the topology of (free boundary) minimal surfaces

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