22 citations · 57 across the 27 of their papers we have counts for
29 papers
The -Null Locus and Local Regularity of Weak Solutions of the Semistable -Equation
Hao Fang, Biao Ma
For the semistable -equation, we prove that the numerical -null locus coincides with the ambient -singular locus of Murakami's weak solution. Consequently, this singular…
Determinantal capacity and -Estimates
Hao Fang, Biao Ma, Jinyang Wu
We introduce determinantal ellipticity, or det-ellipticity, a quantitative structural condition for fully nonlinear elliptic operators on compact Kähler manifolds that provides the…
Liouville Rigidity for Real and Complex Degenerate Hessian Equations
Hao Fang, Biao Ma, Jinyang Wu
We prove Liouville rigidity theorems for translation-invariant real and complex Hessian equations in the viscosity sense, where the PDE is encoded by an admissible set $\mathcal{A}…
Ideal Gårding polynomials
Hao Fang, Biao Ma
We introduce ideal Gårding polynomials, a convexity-enhanced subclass of Gårding polynomials whose Gårding components are recursively convex under partial differentiation. This cla…
Admissibility, Topology, and the -Loewner--Nirenberg problem
Hao Fang, Matthew J. Gursky
The -Loewner--Nirenberg problem is a fully nonlinear generalization of the classical Loewner--Nirenberg problem of constructing complete conformal metrics with constant negati…
A Liouville's theorem for some Monge-Ampère type equations
Hao Fang, Biao Ma, Wei Wei
We study a Monge-Ampère type equation that interpolates the classical {σ_2} -Yamabe equation in conformal geometry and the 2-Hessian equation in dimension 4.