https://neckpinch.com/authors/xin-fu/New arXiv papers by Xin Fu, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2211.09104/arxiv:2211.09104Wed, 16 Nov 2022 00:00:00 GMTVestislav Apostolov, Xin Fu, Jeffrey Streets, Yury Ustinovskiy — We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, which requires a new local Goto/Kodaira-Spencer deformation result, and use it to show that solutions of the generalized Calabi-Yau equation on compact manifolds are classically Kähler, Calabi-Yau, and furthermore unique in their generalized Kähler class. We show that the generalized Kähler-Ricci flow is naturally adapted to this conjecture, and exhibit a number of a priori estimates and monotonicity formulas which suggest global existence and convergence. For initial data in the generalized Kähler class of a Kähler Calabi-Yau structure we prove the flow exists globally and converges to this unique fixed point. This has applications to understanding the space of generalized Kähler structures, and as a special case yields the topological structure of natural classes of Hamiltonian symplectomorphisms on hyperKähler manifolds. In the case of commuting-type generalized Kähler structures we establish global existence and convergence with arbitrary initial data to a Kähler, Calabi-Yau metric, which yields a new d d^c-lemma for these structures.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence