Lifting for manifold-valued maps of bounded variation

Lifting for manifold-valued maps of bounded variation

Let N be a smooth, compact, connected Riemannian manifold without boundary. Let E→N be the Riemannian universal covering of N. For any bounded, smooth domain Ω⊆Rd and any u∈BV(Ω,N), we show that u has a lifting v∈BV(Ω,E). Our result proves a conjecture by Bethuel and Chiron.

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Veröffentlicht in:Journal of functional analysis 2020-06, Vol.278 (10), p.108453, Article 108453
Hauptverfasser: Canevari, Giacomo, Orlandi, Giandomenico
Format: Artikel
Sprache:eng
Schlagworte:
Bounded variation
Lifting problem
Manifold-valued maps
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Zusammenfassung:Let N be a smooth, compact, connected Riemannian manifold without boundary. Let E→N be the Riemannian universal covering of N. For any bounded, smooth domain Ω⊆Rd and any u∈BV(Ω,N), we show that u has a lifting v∈BV(Ω,E). Our result proves a conjecture by Bethuel and Chiron.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.108453