2014/01/08 by Emilio Musso, Lorenzo Nicolodi · 6 citations
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Constant (computer programming) #Curvature #Deformation (meteorology) #Geometric Analysis and Curvature Flows #Holomorphic function #Laguerre polynomials #Quadratic equation #Quartic function #math.DG #msc:53A35 #msc:53C42
paper · pdf · doi:10.1007/s00209-016-1689-7
published in Mathematische Zeitschrift 284(3-4), 1089-1110 (Springer Science+Business Media) · 25 pages
arxiv created 2014/01/08 · openalex publication_date 2016/05/14 · openalex created_date 2016/06/24 · arxiv updated 2017/06/15 · openalex updated_date 2026/08/05
A Laguerre geometric local characterization is given of L-minimal surfaces and Laguerre deformations (T-transforms) of L-minimal isothermic surfaces in terms of the holomorphicity of a quartic and a quadratic differential. This is used to prove that, via their Laguerre Gauss maps, the T-transforms of L-minimal isothermic surfaces have constant mean curvature in some translate of hyperbolic 3-space or de Sitter 3-space in Minkowski 4-space, or have mean curvature zero in some translate of a time-oriented lightcone in Minkowski 4-space. As an application, we show that various instances of the Lawson isometric correspondence can be viewed as special cases of the T-transformation of L-isothermic surfaces with holomorphic quartic differential.