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math.AP2026
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…
math.AP2026
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…
math.AP2026
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}…