2004/03/18 by Martin Schmidt, Martin Ulrich Schmidt, Schmidt, Martin Ulrich
Mathematics · #35P05 #53A05 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #math.AP #math.DG #msc:35P05 #msc:53A05
paper · pdf · doi:10.48550/arxiv.math/0403301
43 pages
arxiv created 2004/03/18 · openalex publication_date 2004/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the class of all conformal mappings from a compact Riemann surface into the threedimensional or fourdimensional Euclidean space. A sequence in this class with bounded Willmore functional is shown to have a sequence of conformal transformations of the target space, such that a subsequence of the transformed sequence converges. This implies that there exists a smooth conformal mapping, which minimizes the Willmore functional in this class. For this purpose we extend the quaternionic function theory of Pedit and Pinkall to square integrable Hopf fields. In particular, we proof the Pluecker formula for such Hopf fields.