Author

Truong Dinh Dat

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Preprint Jul 2026

Stability and strong convergence for complex Hessian equations with $L^1$ data

We study complex $m$-Hessian equations on bounded hyperconvex domains with right-hand side in $L^1(\Omega)$. The main contribution of this paper is a strong stability result for weak solutions in the Hessian energy sense. More precisely, if $f_j \to f$ in $L^1(\Omega)$ and $u_j, u$ are the corresponding solutions, then...

Truong Dinh Dat · 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