On periodic critical points and local minimizers of the Ohta-Kawasaki functional

TL;DR

This paper investigates periodic critical points and local minimizers of a nonlocal isoperimetric problem related to diblock copolymers, demonstrating the construction of such points resembling stable constant mean curvature hypersurfaces.

Contribution

It introduces a variational method to construct periodic critical points with shapes similar to any stable constant mean curvature hypersurface, advancing understanding of the Ohta-Kawasaki functional.

Findings

Construction of locally minimizing periodic critical points

Shape resemblance to stable constant mean curvature hypersurfaces

Auxiliary results of independent mathematical interest

Abstract

In this paper we collect some new observations about periodic critical points and local minimizers of a nonlocal isoperimetric problem, arising in the modeling of diblock copolymers. In the main result, by means of a purely variational procedure, we show that it is possible to construct (locally minimizing) periodic critical points whose shape resemble that of any given strictly stable constant mean curvature (periodic) hypersurface. Along the way, we establish several auxiliary results of independent interest.