Calculus of Variations and Geometric Measure Theory

R. Choksi - I. Topaloglu - G. Tsogtgerel

Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2013

ArXiv: 1311.3512 PDF


On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence of a local minimizer with arbitrary many interfaces in the axisymmetric class of admissible functions. These local minimizers in this restricted class are shown to be critical points in the broader sense (i.e., with respect to all perturbations). We then explore the rigidity, due to curvature effects, in the criticality condition via several quantitative results regarding the axisymmetric critical points.