arXiv subjects

Zhonghua Hou

Publications and source records attributed to Zhonghua Hou.

2 recordsLinked to original sources

arXiv2023

Mean curvature flow solitons from symmetry group viewpoint

The symmetry group of the mean curvature flow in general ambient Riemannian manifolds is determined, based on which we define generalized solitons to the mean curvature flow. We also provide examples of homothetic solitons in non-Euclidean surfaces and prove that all the affine solutions to the mean curvature flow are self-similar solutions.

math.DG↗

arXiv2023

Translation surfaces in Lie groups with constant Gaussian curvature

Let G be a n-dimensional Lie group (n>2) with a bi-invariant Riemannian metric. We prove that if a surface of constant Gaussian curvature in G can be expressed as the product of two curves, then it must be flat. In particular, we can essentially characterize all such surfaces locally in 3-dimensional case.

math.DG↗