On different notions of calibrations for minimal partitions and minimal networks in ℝ22

Marcello Carioni, Alessandra Pluda*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
12 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)401-417
Number of pages17
JournalAdvances in Calculus of Variations
Volume14
Issue number3
DOIs
Publication statusPublished - 1 Jul 2021
Externally publishedYes

Keywords

  • Calibrations
  • currents
  • minimal networks
  • minimal partitions
  • Steiner problem

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