2004/07/01 by Mikhail G. Katz, Katz, Mikhail G., Stephane Sabourau +2
Mathematics · #53C23 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.AG #math.CV #math.DG #msc:53C23
paper · pdf · doi:10.48550/arxiv.math/0407009
9 pages. Proceedings Amer. Math. Soc., to appear
openalex publication_date 2004/07/01 · arxiv created 2004/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that C. Loewner's inequality for the torus is satisfied by all hyperelliptic surfaces X, as well. We first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to X away from the Weierstrass points. The loops are then transplanted to X, and surgered to obtain a Loewner loop on X. In higher genus, we exploit M. Gromov's area estimates for epsilon-regular metrics on X.