3 citations · 4 across the 3 of their papers we have counts for
4 papers
Weak Counterexamples to Curvature Estimates for Minimizing Surfaces
Zhenhua Liu
We construct a sequence of smooth minimizing surfaces in a sequence of metrics converging to the standard Euclidean metric, so that they have diverging norm of second fundame…
Stationary one-sided area-minimizing hypersurfaces with isolated singularities
Zhenhua Liu
We extend the results of Hardt and Simon on area-minimizing cones to prove that isolated singularities of stationary one-sided area-minimizing hypersurfaces can be locally perturbe…
Proof of Bishop's volume comparison theorem using singular soap bubbles
Hubert Bray, Feng Gui, Zhenhua Liu +1
Bishop's volume comparison theorem states that a compact -manifold with Ricci curvature larger than the standard -sphere has less volume. While the traditional proof uses geo…
The Existence of Embedded -Invariant Minimal Hypersurface
Zhenhua Liu
For a compact connected Lie group acting as isometries on a compact orientable Riemannian manifold and cohomogeneity not equal to 0 or 2, we prove the existence of a…