Calculus of Variations and Geometric Measure Theory

G. Canevari - G. Orlandi

Lifting for manifold-valued maps of bounded variation

created by orlandi on 19 Jul 2019
modified by canevari on 29 Jan 2021


Accepted Paper

Inserted: 19 jul 2019
Last Updated: 29 jan 2021

Journal: Journal of Functional Analysis
Volume: 278
Number: 10
Year: 2020
Doi: j.jfa.2019.108453

ArXiv: 1907.06395 PDF
Links: ArXiv


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

Keywords: BV, lifting problem