Mathematical analysis

Engineering

Morse theory

Neumann boundary condition

Minimal surface

Dirichlet distribution

Mathematics

Biology

Index (typography)

Annulus (botany)

Boundary value problem

Computer science

Botany

World Wide Web

Submanifold

Electrical engineering

Free boundary problem

Boundary (topology)

Morse code

Communications in Analysis and Geometry

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.

Index characterization for free boundary minimal surfaces