We study Blaschke–Santaló diagrams associated with the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work under convexity and volume constraints, in both strong (volume exactly one) and weak (volume at most one) form. We discuss some topological (closedness, simply connectedness) and geometric (shape of the boundaries, slopes near the point corresponding to the ball) properties of these diagrams, also providing a list of conjectures.

On Blaschke–Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue

Lucardesi I.;
2022-01-01

Abstract

We study Blaschke–Santaló diagrams associated with the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work under convexity and volume constraints, in both strong (volume exactly one) and weak (volume at most one) form. We discuss some topological (closedness, simply connectedness) and geometric (shape of the boundaries, slopes near the point corresponding to the ball) properties of these diagrams, also providing a list of conjectures.
2022
Lucardesi, I.; Zucco, D.
File in questo prodotto:
File Dimensione Formato  
s10231-021-01113-6.pdf

non disponibili

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - accesso privato/ristretto
Dimensione 2.57 MB
Formato Adobe PDF
2.57 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
1910.04454.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 569.99 kB
Formato Adobe PDF
569.99 kB Adobe PDF Visualizza/Apri

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

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1210930
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 5
social impact