arXiv subjects

Trong-Thuc Phung

Publications and source records attributed to Trong-Thuc Phung.

2 recordsLinked to original sources

arXiv2025

On uniqueness of solutions to complex Monge-Ampère mean field equations

We establish the uniqueness of solutions to complex Monge-Ampère mean field equations when the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.

math.CV↗

arXiv2020

Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

Let $(X,ω)$ be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Ampère equations with right-hand side in $L^p$, $p>1$. Using this we prove that the solutions are Hölder continuous with the same exponent as in the Kähler case \cite{DDGKPZ14}. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

math.CV↗