Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M 2 × ℝ*
Li Chen , Dan-Dan Hu , Jing Mao , Ni Xiang
Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (2) : 297 -310.
Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M 2 × ℝ*
In this paper, for the Lorentz manifold M 2 × ℝ with M 2 a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate its spacelike graphs over compact, strictly convex domains in M 2, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.
Translating surfaces / Mean curvature flow / Lorentz manifolds
| [1] |
|
| [2] |
|
| [3] |
|
| [4] |
|
| [5] |
Chen, L., Mao, J., Xiang, N. and Xu, C., Inverse mean curvature flow inside a cone in warped products, arXiv:1705.04865v3, 2017. |
| [6] |
|
| [7] |
|
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
Stone, A., The mean curvature evolution of graphs, Honour’s Thesis, ANU, 31, 1989. |
| [14] |
|
| [15] |
|
/
| 〈 |
|
〉 |