On the existence and classification of k-Yamabe gradient solitons

2024/10/09 by Maria Fernanda Espinal, Mariel Sáez, Espinal, Maria Fernanda +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Geometric Analysis and Curvature Flows #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2410.06942

Abstract

In this paper we classify rotationally symmetric conformally flat admissible solitons to the k-Yamabe flow, a fully non-linear version of the Yamabe flow. For n≥ 2k we prove existence of complete expanding, steady and shrinking solitons and describe their asymptotic behavior at infinity. For n<2k we prove that steady and expanding solitons are not admissible. The proof is based on the careful analysis of an associated dynamical system.

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