2024/12/03 by Z. Xiong, Xiong, Zhiyao, Xiaokui Yang +3 · 1 citation
Computer Science · Mathematics · #32H02 #53C55 #Advanced Optimization Algorithms Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Equations Stability Results #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2412.02553
openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps between complex manifolds. In this paper, we establish Schwarz lemmas for holomorphic bundle maps between abstract Hermitian holomorphic vector bundles with various positive curvature bounds. As applications, we prove Schwarz lemmas for holomorphic maps between complex manifolds whose curvature tensors are described by the notion ``RC-positivity''. In particular, new diameter and volume comparison theorems are obtained by using Schwarz lemmas.