Spacelike translating solitons of mean curvature flow with forcing term in Lorentzian product spaces: Nonexistence, mean convexity, rigidity and Calabi-Bernstein type results

Abstract

In this paper, we investigate spacelike translating solitons of mean curvature flow with a constant force term in a Lorentzian product space. By applying maximum principles and Liouville-type results, we derive a series of nonexistence results. Under suitable assumptions, we establish the mean convexity property, some rigidity results, and applications in the non-parametric setting.