Abstract
We obtain rigidity results concerning complete noncompact solitons of the mean curvature flow related to a nonsingular Killing vector field $K$ globally defined in a semi-Riemannian space, which can be modeled as a warped product whose base corresponds to a fixed integral leaf of the distribution orthogonal to $K$ and the warping function is equal to $|K|$. Our approach is based on a suitable maximum principle dealing with a notion of convergence to zero at infinity. As application, we study the uniqueness of solutions for the mean curvature flow soliton equation in these ambient spaces.
Acknowledgment
The authors would like to thank the referee for his/her valuable suggestions and useful comments which improved the paper. The second author is partially supported by CNPq, Brazil, grant 301970/2019-0. The third author is partially supported by CAPES, Brazil.
Citation
Jogli G. Araújo. Henrique F. de Lima. Wallace F. Gomes. "On the rigidity of mean curvature flow solitons in certain semi-Riemannian warped products." Kodai Math. J. 46 (1) 62 - 74, March 2023. https://doi.org/10.2996/kmj46105
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