On the existence and classification of $k$-Yamabe gradient solitons

Maria Fernanda Espinal; Mariel Sáez

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arXiv · 2410.06942

On the existence and classification of $k$-Yamabe gradient solitons

Maria Fernanda Espinal·Mariel Sáez

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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 $n\geq 2k$ 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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BibTeX RIS

Maria Fernanda Espinal, Mariel Sáez. 2024-10-09. On the existence and classification of $k$-Yamabe gradient solitons. https://arxiv.org/abs/2410.06942

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