On the index of Fraser–Sargent-type minimal surfaces

Abstract

Fraser–Sargent surfaces are free boundary minimal surfaces in the four-dimensional unit Euclidean ball. Extended infinitely they define immersed minimal surfaces in the Euclidean space. The parts of these surfaces outside the ball are exterior-free boundary minimal surfaces. We prove that they are stable. Independently of it, we find an upper bound on the index of Fraser–Sargent surfaces inside the ball. Also, we provide computational experiments and state a conjecture about an improved index lower bound of the orientable cover of Fraser–Sargent surfaces inside the ball. Finally, based on a similar computational experiment for infinitely extended Fraser–Sargent surfaces, we state a conjecture about their index.