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In this paper we consider finite energy, \ell-equivariant wave maps from1+3-dimensional Minkowski space exterior to the unit ball at the origin intothe 3-sphere. We impose a Dirichlet boundary condition at r=1, which in thiscontext means that the boundary of the unit ball in the domain gets mapped tothe north pole. Each such \ell-equivariant wave map has a fixed integer-valuedtopological degree, and in each degree class there is a unique harmonic map,which minimizes the energy for maps of the same degree. We prove that anarbitrary \ell-equivariant exterior wave map with finite energy scatters to theunique harmonic map in its degree class, i.e., soliton resolution. This extendsthe recent results of the first, second, and fourth authors on the1-equivariant equation to higher equivariance classes, and thus completelyresolves a conjecture of Bizon, Chmaj and Maliborski, who observed thisasymptotic behavior numerically. The proof relies crucially on exterior energyestimates for the free radial wave equation in dimension d = 2 \ell +3, whichare established in a companion paper.

Stable soliton resolution for exterior wave maps in all equivariance classes