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 describe how instability decomposes into contributions from the smooth faces together with additional spectral effects localized along the singular junctions, governed by a natural Steklov-type eigenvalue problem. This analysis reveals new low-index phenomena that do not occur in the smooth setting.