MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Droplet minimizers for an isoperimetric problem with long-range interactions

Marco Cicalese and Emanuele Spadaro


We give a detailed description of the geometry of single droplet patterns in a nonlocal isoperimetric problem. In particular we focus on the sharp interface limit of the Ohta--Kawasaki free energy for diblock copolymers, regarded as a paradigm for those energies modeling physical systems characterized by a competition between short and a long-range interactions. Exploiting fine properties of the regularity theory for minimal surfaces, we extend previous partial results in different directions and give robust tools for the geometric analysis of more complex patterns.


Related publications

2013 Repository Open Access
Marco Cicalese and Emanuele Spadaro

Droplet minimizers of an isoperimetric problem with long-range interactions

In: Communications on pure and applied mathematics, 66 (2013) 8, pp. 1298-1333