Let N be a smooth, compact, connected Riemannian manifold without boundary. Let E be the Riemannian universal covering of N. For any bounded, smooth domain Omega and any u in BV(Omega, N), we show that u has a lifting v in BV(Omega, E). Our result proves a conjecture by Bethuel and Chiron.
Lifting for manifold-valued maps of bounded variation
Canevari, Giacomo
;Orlandi, Giandomenico
2020-01-01
Abstract
Let N be a smooth, compact, connected Riemannian manifold without boundary. Let E be the Riemannian universal covering of N. For any bounded, smooth domain Omega and any u in BV(Omega, N), we show that u has a lifting v in BV(Omega, E). Our result proves a conjecture by Bethuel and Chiron.
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