Prescribed mean curvature flow for noncompact hypersurfaces in Lorentz manifolds

2024/06/07 by Tam, Luen-Fai
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C44 #Secondary 83C30

paper · doi:10.48550/arxiv.2406.04667

Abstract

Motivated by previous study on mean curvature flow and prescribed mean curvature flow on spatially compact space or asymptotically flat spacetime, in this work we will find sufficient conditions for the short time existence of prescribed mean curvature flow on a Lorentz manifold with a smooth time function starting from a complete noncompact spacelike hypersurface. Long time existence and convergence will also be discussed. Results will be applied to study some prescribed mean curvature flows inside the future of the origin in the Minkowski spacetime. Examples of spacetime related to the existence and convergence results near the future null infinity of the Schwarzschild spacetime are also discussed.

Related

• Prescribed mean curvature flow of non-compact space-like Cauchy\n hypersurfaces
• Power Mean Curvature Flow in Lorentzian Manifolds
• A note on inverse mean curvatrue flow in cosmological spacetimes
• Hypersurfaces of prescribed mean curvature in Lorentzian manifolds
• Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ℝⁿ⁺¹₁