The space $ BV\left(\right.S^{2},S^{1}\left.\right) $: minimal connection and optimal lifting

Radu Ignat

doi:10.1016/j.anihpc.2004.07.003

JournalsaihpcVol. 22, No. 3pp. 283–302

The space $B V (S^{2}, S^{1})$ : minimal connection and optimal lifting

Radu Ignat
École normale supérieure, 45, rue D'Ulm, 75230 Paris cedex 05, France; Laboratoire J.-L. Lions, Université P. et M. Curie, BC 187, 4, pl. Jussieu, 75252 Paris cedex 05, France

$The space $ BV\left(\right.S^{2},S^{1}\left.\right) $: minimal connection and optimal lifting cover$

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Abstract

We show that topological singularities of maps in $BV (S^{2}, S^{1})$ can be detected by its distributional Jacobian. As an application, we construct an optimal lifting and we compute its total variation.

Résumé

On montre que le jacobien d'une fonction $u \in BV (S^{2}, S^{1})$ permet de localiser les singularités topologiques de $u$ . On applique ce résultat à la construction d'un relèvement optimal et on calcule sa variation totale.

Cite this article

Radu Ignat, The space $B V (S^{2}, S^{1})$ : minimal connection and optimal lifting. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 3, pp. 283–302

DOI 10.1016/J.ANIHPC.2004.07.003