Calculus of Variations and Geometric Measure Theory
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M. Carioni - A. Pluda

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

created by carioni on 17 May 2018
modified by pluda on 11 Apr 2019


Accepted Paper

Inserted: 17 may 2018
Last Updated: 11 apr 2019

Journal: Adv. Calc. Var.
Year: 2019
Doi: 10.1515/acv-2019-0005


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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