3 citations · 4 across the 18 of their papers we have counts for
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Spectral Gårding Elliptic Equations
Hao Fang, Biao Ma
We study spectral Gårding elliptic equations on compact Kähler manifolds. Smooth solvability is equivalent to the existence of a smooth representative in the admissible domain. The…
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…
Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups
Tamunonye Cheetham-West, Tam Cheetham-West, Biao Ma +2
We prove that, whenever the monodromy maps are fully-punctured, the finite quotients of a fibered hyperbolic -manifold group detect the taut polynomials of the fibered faces of…
Gårding Polynomials
Hao Fang, Biao Ma
We introduce Gårding polynomials, a class of real multivariate polynomials characterized by positivity regions that are invariant under translation by positive vectors and closed u…
Construction of Anosov flows on fibered hyperbolic 3-manifolds
François Béguin, Christian Bonatti, Biao Ma +1
We prove that fibered hyperbolic -manifolds carrying transitive Anosov flows are abundant. More precisely, for every , there is a finite index subgroup~ of $ \mathrm…