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Aspects of Mean Curvature Flow Solitons in Warped Products

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Abstract

In this article, we study mean curvature flow solitons immersed in warped products and we prove some rigidity results for these immersions under assumptions such as integrability and stochastic completeness. We also obtain gap-type and nonexistence results concerning these geometric objects and some applications to self-shrinkers in the Euclidean space, to mean curvature flow solitons in the Euclidean sphere and to translating mean curvature flow solitons in the Euclidean space. Moreover, we provide a lower diameter estimate for mean curvature flow solitons.

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Funding

I. Domingos was supported by the Research Foundation-Flanders (FWO) and the Fonds de la Recherche Scientifique (FNRS) under EOS Project G0H4518N. M. Santos is partially supported by Paraíba State Research Foundation (FAPESQ), Brazil, Grant 3025/2021 and by the National Council for Scientific and Technological Development – CNPq, Brazil, Grant 306524/2022-8.

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  1. Iury Domingos

    Present address: Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, 3001, Leuven, Belgium

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  1. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, Paraíba, 58051-900, Brazil

    Iury Domingos & Márcio Santos

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  1. Iury Domingos
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  2. Márcio Santos
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Domingos, I., Santos, M. Aspects of Mean Curvature Flow Solitons in Warped Products. Results Math 78, 191 (2023). https://doi.org/10.1007/s00025-023-01969-5

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