https://neckpinch.com/authors/duong-h-phong/New arXiv papers by Duong H. Phong, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2304.02533arxiv:2304.02533Wed, 05 Apr 2023 00:00:00 GMTDuong H. Phong — A survey of new geometric flows motivated by string theories is provided. Their settings can range from complex geometry to almost-complex geometry to symplectic geometry. From the PDE viewpoint, many of them can be viewed as intermediate flows between the Ricci flow and the Kähler-Ricci flow, albeit often coupled to flows of additional fields. In particular, a survey is given of joint works of the author with Tristan Collins, Teng Fei, Bin Guo, Sebastien Picard, and Xiangwen Zhang.Ricci flowKähler–Ricci flowKähler geometry https://arxiv.org/abs/2209.09428arxiv:2209.09428Tue, 20 Sep 2022 00:00:00 GMTBin Guo, Duong H. Phong, Jian Song, Jacob Sturm — Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for L^∞ estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.Ricci flowKähler–Ricci flowRicci-flat & Calabi–YauSingularitiesKähler geometryLong-time existence & convergence https://arxiv.org/abs/2111.14048arxiv:2111.14048Sun, 28 Nov 2021 00:00:00 GMTTeng Fei, Duong H. Phong — Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in complex geometry. Examples include the Hitchin gradient flow on symplectic manifolds, and a new flow which is called the dual Ricci flow.Ricci flow