Let us consider two closed homeomorphic manifolds $mathcal{M}$, $mathcal{N}$ of class $C^1$ and two functions $varphi:{mathcal{M}}rightarrow mathbb{R}$, $psi:mathcal{N}rightarrow mathbb{R}$ of class $C^1$. The natural pseudodistance ${d}$ between the pairs $({mathcal{M}},varphi)$, $({mathcal{N}},psi)$ is defined as the infimum of $Theta(f)stackrel{def}{=}max_{Pin mathcal{M}}|varphi(P)-psi(f(P))|$, as $f$ varies in the set of all homeomorphisms from $mathcal{M}$ onto $mathcal{N}$. In this paper we prove that a suitable multiple of ${d}$ by a positive integer $k$ coincides with the distance between two critical values of the functions $varphi,psi$.

Natural pseudodistances between closed manifolds

DONATINI, PIETRO;FROSINI, PATRIZIO
2004

Abstract

Let us consider two closed homeomorphic manifolds $mathcal{M}$, $mathcal{N}$ of class $C^1$ and two functions $varphi:{mathcal{M}}rightarrow mathbb{R}$, $psi:mathcal{N}rightarrow mathbb{R}$ of class $C^1$. The natural pseudodistance ${d}$ between the pairs $({mathcal{M}},varphi)$, $({mathcal{N}},psi)$ is defined as the infimum of $Theta(f)stackrel{def}{=}max_{Pin mathcal{M}}|varphi(P)-psi(f(P))|$, as $f$ varies in the set of all homeomorphisms from $mathcal{M}$ onto $mathcal{N}$. In this paper we prove that a suitable multiple of ${d}$ by a positive integer $k$ coincides with the distance between two critical values of the functions $varphi,psi$.
P. Donatini; P. Frosini
File in questo prodotto:
Eventuali allegati, non sono esposti

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/11585/12212
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 33
social impact