Title: Geometric Stability of Minimal Surfaces with Y-Singularities

Abstract: Singular minimal surfaces arise naturally in geometric variational problems, yet their stability theory remains far less understood than in the smooth setting.
In this talk, I will present geometric stability results for minimal surfaces with Y-singularities in $\mathbb{R}^3$. I will explain how instability decomposes into contributions from the smooth faces and additional spectral effects localized along the singular junctions, which are governed by a natural Steklov-type eigenvalue problem. This analysis reveals new low-index phenomena that do not occur in the smooth setting.