2022/10/07 by Keaton Naff, Naff, Keaton, Jonathan J. Zhu +1
Engineering · Mathematics · #3D Shape Modeling and Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2210.03263
openalex publication_date 2022/10/07 · openalex created_date 2022/10/11 · openalex updated_date 2026/07/28
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ball. These monotonicity formulae involve an energy-like integral over sets which are, in general, not geodesic balls. In the Euclidean case, these sets reduce to the moving-centre balls introduced by the second author in [Zhu18].