Soliton Resolution for Equivariant Wave Maps on a Wormhole

We study finite energy -equivariant wave maps from the (1+3)-dimensional spacetime where the metric on is given by The constant time slices are each given by a Riemannian manifold with two asymptotically Euclidean ends at that are connected by a 2-sphere at r = 0. The spacetime has appeared in the general relativity literature as a prototype wormhole geometry (but is not expected to exist in nature). Each -equivariant finite energy wave map can be indexed by its topological degree n. For each and n, there exists a unique, linearly stable energy minimizing -equivariant harmonic map of degree n. In this work, we prove the soliton resolution conjecture for this model. More precisely, we show that modulo a free radiation term every -equivariant wave map of degree n converges strongly to . This fully resolves a conjecture made by Bizon and Kahl. Previous work by the author proved this result for the corotational case and established many preliminary results that are used in the current work.