The double-bubble problem on the square lattice

Friedrich M, Górny W, Stefanelli U (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Interfaces and Free Boundaries European Mathematical Society

Book Volume: 26

Pages Range: 79-134

Journal Issue: 1

DOI: 10.4171/IFB/510

Abstract

We investigate the minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We give a detailed description of the fine geometry of minimisers, and, in some parameter regime, we compute the optimal perimeter as a function of the size of the point sets. Moreover, we provide a sharp bound on the difference between two minimisers, which are generally not unique, and use it to rigorously identify their Wulff shape as the size of the point sets scales up.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

University of Warsaw / Uniwersytet Warszawski PL Poland (PL) Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M., Górny, W., & Stefanelli, U. (2023). The double-bubble problem on the square lattice. Interfaces and Free Boundaries, 26(1), 79-134. https://doi.org/10.4171/IFB/510

MLA:

Friedrich, Manuel, Wojciech Górny, and Ulisse Stefanelli. "The double-bubble problem on the square lattice." Interfaces and Free Boundaries 26.1 (2023): 79-134.

BibTeX: Download