2015/05/26 by Hideki Miyachi, Miyachi, Hideki
Mathematics · #Complex Variables (math.CV) #Computer science #Corollary #Differential Geometry (math.DG) #FOS: Mathematics #Function (biology) #Geometric Topology (math.GT) #Geometry #Geometry and complex manifolds #Holomorphic and Operator Theory #Mathematical proof #Mathematics #Meromorphic and Entire Functions #Point (geometry) #Pure mathematics #Space (punctuation) #math.CV #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.1505.06785
In this revision, we correct typos and some errors. OLD COMMENT: In the second version, I correct typos and add a disk-convexity result and an alternative approach to Gardiner's formulaIn In this version, I add explanations
openalex publication_date 2015/05/26 · arxiv created 2015/07/25 · arxiv updated 2015/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we show that the extremal length functions on Teichmüller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of L.Liu and W.Su's results on the plurisubharmonicity of extremal length functions. We also obtain alternative proofs of S.Krushkal's results that a function defined by the Teichmüller distance from a reference point is plurisubharmonic, and the Teichmüller space is hyperconvex. To show the log-plurisubharmonicity, we give an explicit formula of the Levi form of the extremal length functions in generic case.