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arXiv · 2109.05247

Translating Solitons to Flows by Powers of The Gaussian Curvature in Riemannian Products

Ronaldo Freire de Lima
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Abstract

We consider translating solitons to flows by positive powers $\alpha$ of the Gaussian curvature -- called $K^\alpha$-flows -- in Riemannian products $M\times\mathbb R.$ We prove that, when $M$ is the Euclidean space $\mathbb R^n,$ the sphere $\mathbb S^n,$ or one of the hyperbolic spaces $\mathbb{H}_{\mathbb F}^m,$ there exist complete rotational translating solitons to $K^\alpha$-flow in $M\times\mathbb R$ for certain values of $\alpha.$

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Ronaldo Freire de Lima. 2021-09-11. Translating Solitons to Flows by Powers of The Gaussian Curvature in Riemannian Products. https://arxiv.org/abs/2109.05247

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