Author

Dat Dinh Truong

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Preprint Sep 2026

A Pluripotential-Theoretic Approach to Finiteness of Polarized Calabi--Yau Manifolds

We propose a pluripotential-theoretic framework for studying finiteness questions for polarized Calabi--Yau manifolds. The central idea is to use global $m$-Hessian capacities as a quantitative intermediate between complex potential theory and global geometric boundedness. We formulate a chain of uniform estimates co...

Dat Dinh Truong · 0 citations

Preprint Sep 2026

Relative Finite Energy Classes for Complex Hessian Equations with Prescribed Singularities

Let $\Omega\subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and let $\psi\in SH_m(\Omega)$ be a fixed negative $m$-subharmonic function. In this paper we introduce a relative finite energy class $\mathcal E_{m,\psi}(\Omega),$ which may be viewed as a Hessian analogue of the relative energy classes appearing in...

Dat Dinh Truong · 0 citations

Preprint Sep 2026

An $m$-Hessian approach to Yau uniformization conjecture

We develop an $m$-Hessian approach to the construction of finite-Monge--Amp\`ere weights on complete noncompact K\"ahler manifolds. Let $(M^n,g)$ be a complete noncompact K\"ahler manifold of complex dimension $n\ge3$ with positive holomorphic bisectional curvature. The main new ingredient is a quantitative capac...

Dat Dinh Truong · 0 citations

Preprint Jul 2026

Uniform $L^\infty$ estimates for complex hessian equations on compact Hermitian manifolds

We develop a pluripotential approach to complex Hessian equations on compact Hermitian manifolds. In this setting, the lack of closedness of the background metric introduces torsion terms that prevent a direct extension of the K\"ahler theory. Our main result is a uniform $L^\infty$ estimate for bounded $\omega$-$m$-su...

Dat Dinh Truong · 0 citations