2023/04/04 by Emanuel Indrei, Indrei, Emanuel, Aram Karakhanyan +1
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2304.01866
openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the sharp quantitative stability in the radial isotropic Almgren problem. In addition, we develop a theory for estimating the sharp modulus in the context of minimal assumptions on the surface tension and the potential and obtain the sharp ε2 in any dimension. Inter-alia, we also solve the problem of calculating the critical mass which was only a priori assumed to exist and which breaks the mass regime into two sets: the one where the energy is concave and the one where it is convex.