2020/01/17 by Gabriel Khan, Jun Zhang, Khan, Gabriel +3
Mathematics · Medicine · #32Q10 #49Q20 #53B35 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries
paper · pdf · doi:10.48550/arxiv.2001.06155
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study a class of Kähler manifolds defined on tube domains in ℂn, and in particular those which have O(n) × ℝn symmetry. For these, we prove a uniqueness result showing that any such manifold which is complete and has non-negative orthogonal bisectional curvature (n ≥ 3) or non-negative bisectional curvature (n ≥ 2) is biholomorphically isometric to ℂn. We also consider another curvature tensor called the orthogonal anti-bisectional curvature. We find necessary and sufficient conditions for a complete O(n)-symmetric tube domain to have non-negative orthogonal anti-bisectional curvature and provide several examples of complete metrics which satisfy this condition. Finally, we discuss some applications of these spaces within optimal transport. In particular, we study "synthetic" curvature bounds for non-smooth geometries and how they can be applied to the rough geometry induced by the Monge cost c(x,y)=‖x-y‖.