A computer study of clusters of up to N = 200 000 equal-area bubbles shows for the first time that partially rounding conjectured optimal hexagonal planar soap bubble clusters reduces perimeter. Different methods of creating optimal clusters are compared, and new candidate minimizers for several N are given.</p
We consider the soap bubble problem on the sphere S2, which seeks a perimeter-minimizing partition ...
13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer...
We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minim...
A computer study of clusters of up to N = 200 000 equal-area bubbles shows for the first time that p...
Candidates to the least perimeter partition of various polygonal shapes into N planar connected equa...
Candidates to the least perimeter partition of the surface of a sphere into N planar connected regio...
Candidates to the least perimeter partition of a disk into N planar connected regions are calculated...
We present conjectured candidates for the least perimeter partition of a disc into N≤10 connected re...
We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and ca...
We prove that the standard double bubble provides the least-area way to enclose and separate two reg...
• The conjectured least perimeter partition is given for bubbles of unit area, including the boundar...
We assess the stability of simple two-dimensional clusters of bubbles relative to small displacement...
In this thesis we analyze the problem of the global shape of perimeter-minimizing planar N-clusters,...
We investigate the equilibrium properties of a single area-minimising bubble trapped between two nar...
In this paper, we investigate some properties of planar soap bubbles on a straight wall with a singl...
We consider the soap bubble problem on the sphere S2, which seeks a perimeter-minimizing partition ...
13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer...
We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minim...
A computer study of clusters of up to N = 200 000 equal-area bubbles shows for the first time that p...
Candidates to the least perimeter partition of various polygonal shapes into N planar connected equa...
Candidates to the least perimeter partition of the surface of a sphere into N planar connected regio...
Candidates to the least perimeter partition of a disk into N planar connected regions are calculated...
We present conjectured candidates for the least perimeter partition of a disc into N≤10 connected re...
We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and ca...
We prove that the standard double bubble provides the least-area way to enclose and separate two reg...
• The conjectured least perimeter partition is given for bubbles of unit area, including the boundar...
We assess the stability of simple two-dimensional clusters of bubbles relative to small displacement...
In this thesis we analyze the problem of the global shape of perimeter-minimizing planar N-clusters,...
We investigate the equilibrium properties of a single area-minimising bubble trapped between two nar...
In this paper, we investigate some properties of planar soap bubbles on a straight wall with a singl...
We consider the soap bubble problem on the sphere S2, which seeks a perimeter-minimizing partition ...
13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer...
We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minim...
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