Calculus of Variations and Geometric Measure Theory
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G. Canevari - G. Orlandi

Lifting for manifold-valued maps of bounded variation

created by orlandi on 19 Jul 2019

[BibTeX]

Submitted Paper

Inserted: 19 jul 2019

Pages: 15
Year: 2019
Links: ArXiv

Abstract:

Let $N$ be a smooth, compact, connected Riemannian manifold without boundary. Let $E\to N$ be the Riemannian universal covering of $N$. For any bounded, smooth domain $Ω\subset ℝ^d$ and any $u\in BV(Ω,N)$, we show that $u$ has a lifting $v\in BV(Ω,E)$. Our result proves a conjecture by Bethuel and Chiron.

Keywords: BV, lifting problem

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