Index characterization for free boundary minimal surfaces

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Abstract

In this paper, we compute the Morse index of a free boundary minimal submanifold from data of two simpler problems. The first is the fixed boundary problem and the second is concered with the Dirichlet-to-Neumann map associated with the Jacobi operator. As an application, we show that the Morse index of a free boundary minimal annulus is equal to 4 if and only if it is the critical catenoid.

Original languageEnglish
Pages (from-to)189-222
Number of pages34
JournalCommunications in Analysis and Geometry
Volume28
Issue number1
DOIs
StatePublished - 2020

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