https://neckpinch.com/authors/quang-tuan-dang/New arXiv papers by Quang-Tuan Dang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2603.25520arxiv:2603.25520Thu, 26 Mar 2026 00:00:00 GMTQuang-Tuan Dang — We study the stability and Hölder continuity of solutions to degenerate complex Monge–Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern–Ricci flow.Ricci flowGeneralized & G₂ flowsKähler geometryStability & uniqueness https://arxiv.org/abs/2404.01126arxiv:2404.01126Mon, 01 Apr 2024 00:00:00 GMTQuang-Tuan Dang — We establish a transcendental generalization of Nakamaye's theorem to compact complex manifolds when the form is not assumed to be closed. We apply the recent analytic technique developed by Collins and Tosatti to show that the non-Hermitian locus of a nef and big (1,1)-form, which is not necessarily closed, on a compact complex manifold equals the union of all positive-dimensional analytic subvarieties where the restriction of the form is not big (null locus). As an application, we can give an alternative proof of the Nakai–Moishezon criterion of Buchdahl and Lamari for complex surfaces and generalize this result in higher dimensions Finally, we investigate finite time non-collapsing singularities of the Chern–Ricci flow, partially answering a question raised by Tosatti and Weinkove.Ricci flowGeneralized & G₂ flowsSingularities(Non)collapsingAnalytic minimal model program https://arxiv.org/abs/2305.16461arxiv:2305.16461Thu, 25 May 2023 00:00:00 GMTQuang-Tuan Dang — We study the nature of finite-time singularities for the Chern-Ricci flow, partially answering a question of Tosatti-Weinkove. We show that a solution of degenerate parabolic complex Monge-Ampère equations starting from arbitrarily positive (1,1)-currents are smooth outside some analytic subset, generalizing works by Di Nezza-Lu. We extend Guedj-Lu's recent approach to establish uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Hermitian manifolds. We apply it to studying the Chern-Ricci flows on complex log terminal varieties starting from an arbitrary current.Ricci flowGeneralized & G₂ flowsSingularitiesKähler geometryAnalytic minimal model program https://arxiv.org/abs/2201.01150arxiv:2201.01150Mon, 03 Jan 2022 00:00:00 GMTQuang-Tuan Dang — Extending a recent theory developed on compact Kähler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Ampère equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time and continuous in space and that such a solution is unique. We also establish a partial regularity of such solutions under some extra assumptions of the densities and apply it to prove the existence and uniqueness of the weak Chern-Ricci flow on complex compact varieties with log terminal singularities.Ricci flowGeneralized & G₂ flowsSingularitiesKähler geometryStability & uniquenessAnalytic minimal model program