2022/05/05 by Maggi, Francesco, Novack, Michael · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2205.02951
We obtain a full resolution result for minimizers in the exterior isoperimetric problem with respect to a compact obstacle in the large volume regime v→∞. This is achieved by the study of a Plateau-type problem with free boundary (both on the compact obstacle and at infinity) which is used to identify the first obstacle-dependent term (called \it isoperimetric residue) in the energy expansion, as v→∞, of the exterior isoperimetric problem. A crucial tool in the analysis of isoperimetric residues is a new mesoscale flatness criterion for hypersurfaces with bounded mean curvature, which we obtain as a development of ideas originating in the theory of minimal surfaces with isolated singularities.