Morse index of y-singular minimal surfaces

TL;DR

This paper calculates the Morse index of rotationally symmetric Y-singular minimal surfaces with a single circle of singularities, using simpler related problems, and finds that the Y-catenoid has an index of one.

Contribution

It introduces a method to compute the Morse index of Y-singular minimal surfaces by relating it to simpler boundary and stability problems.

Findings

The Morse index of the Y-catenoid is one.

The computation relies on analyzing fixed boundary problems and the Dirichlet-to-Neumann map.

The approach simplifies the index calculation for singular minimal surfaces.

Abstract

In this paper, we compute the Morse index of rotationally symmetric minimal Y-singular surfaces under assumption that the Y-singularities form a single circle. This computation is carried out by utilizing information from two simpler problems: the first deals with the fixed boundary problem on singularities, and the second focuses on the Dirichlet-to-Neumann map associated with the stability operator. Notably, our findings reveal that the index of the Y -catenoid is one.