Inserted: 19 jul 2019
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