2018/08/31 by Sascha Eichmann
Mathematics · #Boundary (topology) #Boundary value problem #Convergence (economics) #Counterexample #Dirichlet problem #Energy (signal processing) #Energy functional #Geometric Analysis and Curvature Flows #Immersion (mathematics) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35J35 #msc:35J40 #msc:49Q10 #msc:49Q20 #msc:58J32
paper · pdf · doi:10.1007/s00526-018-1468-x
published as Calculus of Variations and Partial Differential Equations, 58:34, 2019 · 28 pages, 3 figures
openalex created_date 2018/08/22 · arxiv created 2018/09/28 · openalex publication_date 2019/01/07 · arxiv updated 2019/09/06 · openalex updated_date 2026/08/05
We construct a branched Helfrich immersion satisfying Dirichlet boundary conditions. The number of branch points is finite. We proceed by a variational argument and hence examine the Helfrich energy for oriented varifolds. The main contribution of this paper is a lower-semicontinuity result with respect to oriented varifold convergence for the Helfrich energy and a minimising sequence. For arbitrary sequences this is false by a counterexample of Große-Brauckmann.