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<p>We investigate translating solitons of the mean curvature flow immersed in a class of warped products obeying standard curvature constraints, which includes the Euclidean, pseudo-hyperbolic, Schwarzschild and Reissner-Nordström spaces. Initially, we establish a suitable version of the Omori-Yau maximum principle related to a specific drift Laplacian, enabling us to obtain a nonexistence result concerning these translating solitons. Afterwards, we apply a parabolicity criterion and a Liouville type result to establish rigidity theorems for complete translating solitons, in the sense that they must be totally geodesic. Finally, we study entire translating graphs in our class of warped products obtaining new Moser-Bernstein type results.</p>

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Translating solitons of the mean curvature flow in warped products: nonexistence and rigidity

  • 期刊论文

  • 发表日期：

    2025年6月14日

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  • Cícero P. Aquino,
  • Henrique F. de Lima,
  • Gustavo S. Dias

摘要

We investigate translating solitons of the mean curvature flow immersed in a class of warped products obeying standard curvature constraints, which includes the Euclidean, pseudo-hyperbolic, Schwarzschild and Reissner-Nordström spaces. Initially, we establish a suitable version of the Omori-Yau maximum principle related to a specific drift Laplacian, enabling us to obtain a nonexistence result concerning these translating solitons. Afterwards, we apply a parabolicity criterion and a Liouville type result to establish rigidity theorems for complete translating solitons, in the sense that they must be totally geodesic. Finally, we study entire translating graphs in our class of warped products obtaining new Moser-Bernstein type results.