2010/04/15 by Francisco J. López, Francisco J. Lopez, Lopez, Francisco J.
Mathematics · #49Q05 (Secondary) #49Q10 #53A10 (Primary) #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG #msc:49Q05 #msc:49Q10 #msc:53A10 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1004.2656
16 pages, 3 figures
arxiv created 2010/04/15 · openalex publication_date 2010/04/15 · arxiv updated 2010/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a general fusion theorem for complete orientable minimal surfaces in ℝ3 with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are produced. More specifically, universal surfaces (i.e., surfaces from which all minimal surfaces can be recovered) and space-filling surfaces with arbitrary genus and no symmetries.