https://neckpinch.com/authors/kuan-hui-lee/New arXiv papers by Kuan-Hui Lee, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2601.03092arxiv:2601.03092Tue, 06 Jan 2026 00:00:00 GMTKuan-Hui Lee — In this work, we discuss the stability of Donaldson's flow of surfaces in a hyperkähler 4-manifold. In, Wang and Tsai proved a uniqueness theorem and C¹ dynamic stability theorem of the mean curvature flow for minimal surface. We extend their results and obtain a similar dynamic stability theorem of the hyperkähler flow.Mean curvature flowRicci-flat & Calabi–Yau4-manifoldsKähler geometryStability & uniquenessMinimal & CMC surfaces https://arxiv.org/abs/2504.12525arxiv:2504.12525Wed, 16 Apr 2025 00:00:00 GMTKuan-Hui Lee — In this work, we discuss the stability of the pluriclosed flow and generalized Ricci flow. We proved that if the second variation of generalized Einstein–Hilbert functional is nonpositive and the infinitesimal deformations are integrable, the flow is dynamically stable. Moreover, we prove that the pluriclosed steady solitons are dynamically stable when the first Chern class vanishes.Ricci flowGeneralized & G₂ flowsRicci solitonsStability & uniqueness https://arxiv.org/abs/2303.00149arxiv:2303.00149Wed, 01 Mar 2023 00:00:00 GMTKuan-Hui Lee — The generalized Einstein Hilbert action is an extension of the classic scalar curvature energy and Perelman F functional which incorporates a closed three-form. The critical points are known as generalized Ricci solitons, which arise naturally in mathematical physics, complex geometry, and generalized geometry. Through a delicate analysis of the group of generalized gauge transformations, and implementing a novel connection, we give a simple formula for the second variation of this energy which generalizes the Lichnerowicz operator in the Einstein case. As an application, we show that all Bismut flat manifolds are linearly stable critical points, and admit nontrivial deformations arising from Lie theory. Furthermore, this leads to extensions of classic results of Koiso and Podesta, Spiro, Kröncke to the moduli space of generalized Ricci solitons. To finish we classify deformations of the Bismut-flat structure on S3 and show that some are integrable while others are not.Generalized & G₂ flowsRicci solitonsPerelman entropyScalar curvatureStability & uniqueness https://arxiv.org/abs/2201.02264arxiv:2201.02264Thu, 06 Jan 2022 00:00:00 GMTKuan-Hui Lee — In this paper, I computed the second variation formula of the generalized Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumption. In the last part of the paper, I prove that dynamical stability and linear stability are equivalent on a steady gradient generalized Ricci soliton (g, H,f) which generalizes the result done by Kröncke, Haslhofer, Sesum, Raffero, and Vezzoni.Generalized & G₂ flowsRicci solitonsEinstein metricsStability & uniqueness