Least-perimeter partitions of the disk into three regions of given areas

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We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in three balanced constant geodesic curvature curves meeting themselves at 120 degrees, and reaching orthogonally the boundary of the disk.
19 pages, 8 figures

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Differential Geometry, 49Q10 (Primary) 51M25 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/68079

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0307207
 http://arxiv.org/abs/math/0307207

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arXiv