On different notions of calibrations for minimal partitions and minimal networks in ℝ2-Reference-Cited by-同舟云学术

On different notions of calibrations for minimal partitions and minimal networks in ℝ2

Published:2019-04-06 Issue:3 Volume:14 Page:401-417
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Carioni Marcello¹,Pluda Alessandra²^ORCID

Affiliation:

1. Institut für Mathematik , Universität Graz , Heinrichstraße 36, 8010 Graz , Austria

2. Dipartimento di Matematica , Università di Pisa , Largo Bruno Pontecorvo 5, 56127 Pisa , Italy

Abstract

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 the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2019-0005/pdf

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