@article{Batista2023, 
author = {Márcio Batista and Giovanni Molica Bisci and Henrique de Lima},
title = {Spacelike translating solitons of the mean curvature flow in Lorentzian product spaces with density},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-18},
keywords = {weighted Lorentzian product spaces, Bakry-Émery-Ricci tensor, drift Laplacian, f-mean curvature, mean curvature flow, spacelike translating solitons, Gaussian space},
url = {https://www.sciopen.com/article/10.3934/mine.2023054},
doi = {10.3934/mine.2023054},
abstract = {By applying suitable Liouville-type results, an appropriate parabolicity criterion, and a version of the Omori-Yau's maximum principle for the drift Laplacian, we infer the uniqueness and nonexistence of complete spacelike translating solitons of the mean curvature flow in a Lorentzian product space              R        1    ×            P        f    n   endowed with a weight function    f and whose Riemannian base              P        n   is supposed to be complete and with nonnegative Bakry-Émery-Ricci tensor. When the ambient space is either              R        1    ×            G        n  , where              G        n   stands for the so-called    n-dimensional Gaussian space (which is the Euclidean space              R        n   endowed with the Gaussian probability measure) or              R        1    ×            H        f    n  , where              H        n   denotes the standard    n-dimensional hyperbolic space and    f is the square of the distance function to a fixed point of              H        n  , we derive some interesting consequences of our uniqueness and nonexistence results. In particular, we obtain nonexistence results concerning entire spacelike translating graphs constructed over              P        n  .}
}