Stable soliton resolution for equivariant wave maps exterior to a ball (Q344577)

This article is based on three articles by C. Kenig, Baoping Liu, and W. Schlag written in collaboration with the author. In this article, the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in \(\mathbb{R}^3\) and taking values in the 3-sphere is reviewed. This conjecture was verified for 1-equivariant exterior wave maps with topological degree \(n = 0\) by the author, and \textit{W. Schlag} [Adv. Math. 232, No. 1, 57--97 (2013; Zbl 1264.35045)], for \(\ell= 1\) and all topological degrees \(n\geq 0\) by \textit{C. E. Kenig} et al. [Geom. Funct. Anal. 24, No. 2, 610--647 (2014; Zbl 1288.35356)], and finally for all remaining equivaraince classes \(\ell\geq2\) by \textit{C. Kenig} et al. [Adv. Math. 285, 235--300 (2015; Zbl 1331.35076)].