On the existence and classification of k-Yamabe gradient solitons

Wed, 09 Oct 2024 00:00:00 GMT

Maria Fernanda Espinal, Mariel Sáez — 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.

Maria Fernanda Espinal — Neckpinch

On the existence and classification of k-Yamabe gradient solitons