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math.DG2025
Existence of Minimal Surfaces in Infinite Volume Hyperbolic 3-manifolds
Baris Coskunuzer, Zheng Huang, Ben Lowe +1
The existence of embedded minimal surfaces in non-compact 3-manifolds remains a largely unresolved and challenging problem in geometry. In this paper, we address several open cases…
math.DG2023
Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds
Zheng Huang, Longzhi Lin, Zhou Zhang
There has been a conjecture, often attributed to Thurston, which asserts that every almost Fuchsian manifold is foliated by closed incompressible constant mean curvature (CMC) surf…
math.DG2023
Uniqueness and non-uniqueness for the asymptotic Plateau problem in hyperbolic space
Zheng Huang, Ben Lowe, Andrea Seppi
We prove several results on the number of solutions to the asymptotic Plateau problem in . Firstly we discuss criteria that ensure uniqueness. Given a Jordan curve …