On different notions of calibrations for minimal partitions and minimal networks in $\mathbb{R}^2$

Marcello Carioni; Alessandra Pluda

doi:10.1515/acv-2019-0005

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arXiv · 1805.11397

On different notions of calibrations for minimal partitions and minimal networks in $\mathbb{R}^2$

Marcello Carioni·Alessandra Pluda

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Abstract

Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner Problem and for planar minimal partitions. The paper is then complemented with remarks on the convexification of the problem, on non-existence of calibrations and on calibrations in families.

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Marcello Carioni, Alessandra Pluda. 2018-05-29. On different notions of calibrations for minimal partitions and minimal networks in $\mathbb{R}^2$. https://doi.org/10.1515/acv-2019-0005

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