The concept of an i-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of i-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.

Symmetrization in geometry / Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 36:(2017), pp. 51-88. [10.1016/j.aim.2016.10.003]

Symmetrization in geometry

BIANCHI, GABRIELE;GRONCHI, PAOLO
2017

Abstract

The concept of an i-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of i-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.
2017
36
51
88
Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo
File in questo prodotto:
File Dimensione Formato  
Steiner34_with_corrections_on_proofs.pdf

Open Access dal 02/01/2020

Descrizione: articolo principale
Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Creative commons
Dimensione 422.43 kB
Formato Adobe PDF
422.43 kB Adobe PDF
Bianchi_Gardner_Gronchi_symmetrizations_in_geometry_online_version.pdf

Accesso chiuso

Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 678.24 kB
Formato Adobe PDF
678.24 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1081671
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 23
social impact