Index characterization for free boundary minimal surfaces
Hung Tran
Abstract
In this paper, we compute the Morse index for a free boundary minimal submanifold from data of two simpler problems. The first one is the corresponding problem with fixed boundary condition; and the second is associated with the Dirichlet-to-Neumann map for Jacobi fields. 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.
Topics & Concepts
Morse codeMathematicsBoundary (topology)Minimal surfaceAnnulus (botany)Mathematical analysisIndex (typography)Characterization (materials science)Morse theoryFree boundary problemBoundary value problemGeometryFixed-point indexPure mathematicsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsNonlinear Partial Differential Equations