Linear Stability of the Self-Similarly Shrinking Lens

Explore the linear stability analysis of self-similarly shrinking lens configurations in this mathematical physics lecture from the Erwin Schrödinger International Institute. Delve into the theoretical framework of parabolic blowup analysis for singularities in 2D multiphase mean curvature flow, where self-similar shrinkers emerge as networks evolving through shrinking homotheties. Examine how these structures function as critical points of entropy defined by interface length functionals with Gaussian weighting, and understand the entropy decrease principle during flow evolution. Learn about the complexities of dynamic stability analysis, particularly addressing the four generically unstable modes that arise from dilation, translation, and rotation transformations. Follow a detailed demonstration of linear stability methodology specifically applied to the lens geometry, gaining insights into advanced techniques for analyzing geometric evolution problems in mathematical physics and differential geometry.