2023/11/20 by Yoshinori Hashimoto, Hashimoto, Yoshinori
Mathematics · #32Q26 (Secondary) #53C55 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2311.11612
openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first three sections of this paper are a survey of the author's work on balanced metrics and stability notions in algebraic geometry. The last section is devoted to proving the well-known result that a geodesically convex function on a complete Riemannian manifold admits a critical point if and only if its asymptotic slope at infinity is positive, where we present a proof which relies only on the Hopf--Rinow theorem and extends to locally compact complete length metric spaces.