Abstract
We give the first existence and regularity results on the cheapest way to enclose and separate planar regions of prescribed areas, where cost is given by a general norm ϕ, thus generalizing the Wulff shape for enclosing a single region. As an example, we classify the cheapest way to enclose and separate two planar regions of prescribed areas for the ℓ1 norm (“Manhattan metric”) into three distinct types, according to the relative size of the prescribed areas.
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Morgan, F., French, C. & Greenleaf, S. Wulff clusters inR 2 . J Geom Anal 8, 97–115 (1998). https://doi.org/10.1007/BF02922110
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DOI: https://doi.org/10.1007/BF02922110