2020/02/12 by Ryosuke Takahashi, Takahashi, Ryosuke · 1 citation
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 53C55 #Secondary 53C44
paper · pdf · doi:10.48550/arxiv.2002.05132
openalex publication_date 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang-Mills (dHYM) metrics. This new property compensates for the lack of concavity of the Lagrangian phase operator as long as the metric is almost calibrated. As an application, we introduce the tangent Lagrangian phase flow (TLPF) on the space of almost calibrated (1,1)-forms that fits into the GIT framework for dHYM metrics recently discovered by Collins-Yau. The TLPF has some special properties that are not seen for the line bundle mean curvature flow (i.e. the mirror of the Lagrangian mean curvature flow for graphs). We show that the TLPF starting from any initial data exists for all positive time. Moreover, we show that the TLPF converges smoothly to a dHYM metric assuming the existence of a C-subsolution, which gives a new proof for the existence of dHYM metrics in the highest branch.