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- W3106304277 abstract "In this paper, we initiate the study of finite energy equivariant wave maps from the (1+3)-dimensional spacetime $mathbb R times (mathbb R times mathbb{S}^2) rightarrow mathbb{S}^3$ where the metric on $mathbb R times (mathbb R times mathbb{S}^2)$ is given by ds^2 = -dt^2 + dr^2 + (r^2 + 1) left ( d theta^2 + sin^2 theta d varphi^2 right ), quad t,r in mathbb{R}, (theta,varphi) in mathbb{S}^2. The constant time slices are each given by the Riemannian manifold $mathcal M := mathbb R times mathbb{S}^2$ with metric ds^2 = dr^2 + (r^2 + 1) left ( d theta^2 + sin^2 theta d varphi^2 right ). The Riemannian manifold $mathcal M$ contains two asymptotically Euclidean ends at $r rightarrow pm infty$ that are connected by a spherical throat of area $4 pi^2$ at $r = 0$. The spacetime $mathbb R times mathcal M$ is a simple example of a wormhole geometry in general relativity. In this work we will consider 1--equivariant or corotational wave maps. Each corotational wave map can be indexed by its topological degree $n$. For each $n$, there exists a unique energy minimizing corotational harmonic map $Q_{n} : mathcal M rightarrow mathbb{S}^3$ of degree $n$. In this work, we show that modulo a free radiation term, every corotational wave map of degree $n$ converges strongly to $Q_{n}$. This resolves a conjecture made by Bizon and Kahl in the corotational case." @default.
- W3106304277 created "2020-11-23" @default.
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- W3106304277 date "2017-10-23" @default.
- W3106304277 modified "2023-09-26" @default.
- W3106304277 title "Soliton Resolution for Equivariant Wave Maps on a Wormhole" @default.
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- W3106304277 doi "https://doi.org/10.1007/s00220-017-3009-4" @default.
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