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Soliton Resolution for Equivariant Wave Maps on a Wormhole

机译:孤独的虫子上的孤子分辨率的虫子

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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.
机译:我们研究了来自(1 + 3) - 二维时期的有限能量的波图,其中由恒定时间切片给出的度量件由riemananian歧管给出,其中两个渐近的欧几里德末端通过2范围连接在r = 0处。作为原型虫洞几何形状的通用相对论文献中出现了空间(但预计本质上不存在)。每个 - 衡量的有限能量波图可以通过其拓扑度n索引。对于每个和n,存在独特的线性稳定的能量,最小化 - Q时Quivariant谐波映射。在这项工作中,我们证明了该模型的孤子解决猜想。更确切地说,我们表明模型是一个自由辐射术语,每个程度Nequivariant波映射强烈收敛到。这完全解决了百on和Kahl制造的猜想。上一份工作提交人证明了核心案件的这一结果,并建立了当前工作中使用的许多初步结果。

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