2014/05/28 by Otis Chodosh, Davi Máximo, Davi Maximo
Mathematics · #Bounded function #Combinatorics #Computer science #Curvature #Function (biology) #Genus #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Index (typography) #Mathematical analysis #Mathematics #Mean curvature #Minimal surface #Pure mathematics #Surface (topology) #Topology (electrical circuits) #Upper and lower bounds #math.AP #math.DG
paper · pdf · doi:10.4310/jdg/1478138547
arxiv created 2014/05/28 · openalex publication_date 2016/11/01 · arxiv updated 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that for an immersed two-sided minimal surface in ℝ3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in ℝ3 of index 2, as conjectured by Choe. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface.