Geodesic
The double-bubble problem on the square lattice
Manuel Friedrich1 orcid ; Wojciech Górny2 orcid ; Ulisse Stefanelli3 orcid
1Friedrich-Alexander Universität Erlangen-Nürnberg, Germany
2University of Vienna, Austria; University of Vienna, Austria
3University of Vienna, Austria
Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 79-134

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DOI

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.
DOI : 10.4171/ifb/510
Classification : 49-XX
Mots-clés : double bubble, square lattice, optimal point configuration, Wulff shape

Manuel Friedrich  1   ; Wojciech Górny  2   ; Ulisse Stefanelli  3

1 Friedrich-Alexander Universität Erlangen-Nürnberg, Germany
2 University of Vienna, Austria; University of Vienna, Austria
3 University of Vienna, Austria 
Manuel Friedrich; Wojciech Górny; Ulisse Stefanelli. The double-bubble problem on the square lattice. Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 79-134. doi: 10.4171/ifb/510
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