2018/08/21 by Teng Fei, Bin Guo, Duong H. Phong · 1 citation
Mathematics · #Convergence (economics) #Energy (signal processing) #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric (unit) #Monotonic function #Nonlinear Partial Differential Equations #Uniform convergence #math.AP #math.DG
paper · pdf · doi:10.1007/s00209-019-02272-2
published as Mathematische Zeitschrift 292(1-2), 473-497 (2019)
arxiv created 2018/08/21 · openalex created_date 2018/08/31 · openalex publication_date 2019/03/13 · arxiv updated 2020/11/10 · openalex updated_date 2026/08/05
A one-parameter family of coupled flows depending on a parameter κ>0 is introduced which reduces when κ=1 to the coupled flow of a metric ω with a (1,1)-form α due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for κ\not=1, estimates for derivatives of all orders would follow from C0 estimates for ω and α. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow in some situations, including on Riemann surfaces. Very little is known as yet about the monotonicity and convergence of flows in presence of couplings, and conditions such as κ\not=1 seem new and may be useful in the future.