3 citations · 4 across the 6 of their papers we have counts for
9 papers · 1 filter
Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces
Zhenhua Liu
We prove that area-minimizing submanifolds in mod homology are not generically smooth, except in the case of geodesics, minimal surfaces and minimal hypersurfaces. This settles…
Area-minimizing surfaces with fractal singular sets: prevalence, moduli space, and refinements on strata
Zhenhua Liu
This paper is a continuation of our work on a conjecture of Almgren on area-minimizing surfaces with fractal singular sets. First, we prove that area-minimizing surfaces with fract…
Area-minimizing submanifolds are not generically smooth
Zhenhua Liu
We prove that area-minimizing submanifolds are not generically smooth, settling a conjecture of White that asks the generic smoothness of area-minimizing submanifolds. We furthermo…
Every finite graph arises as the singular set of a compact -d calibrated area minimizing surface
Zhenhua Liu
Given any (not necessarily connected) combinatorial finite graph and any compact smooth -manifold with the third Betti number , we construct a calibrated 3-dime…
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…