Lower bounds on the energy of maps
type: Item
instance of: scholarly article
title: Lower bounds on the energy of maps
zbMATH Open document ID: 0634.53042
DOI: 10.1215/S0012-7094-87-05544-X
author: Christopher B. Croke
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let f be a smooth map from \({\mathbb{R}}P\) n with the standard metric to an arbitrary Riemannian manifold N and denote by E(f) its energy. The author proves \[ E(f)\geq (L/\pi)^ 2\cdot E(Id_{{\mathbb{R}}P\quad n}) \] where L is the length of the shortest closed geodesic on N in the homotopy class \(f_*\mu\), \(0\neq \mu \in \pi_ 1({\mathbb{R}}P\) n). In particular, the identity map of \({\mathbb{R}}P\) n is energy-minimizing in its homotopy class.
reviewed by: Thomas Friedrich
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 4032551
zbMATH Keywords: energy-minimizing map
zbMATH Keywords: energy
zbMATH Keywords: closed geodesic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4032551