The Helfrich boundary value problem

  • Sascha EichmannEmail author


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.

Mathematics Subject Classification

35J35 35J40 58J32 49Q20 49Q10 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematisch-Naturwissenschaftliche FakultätEberhard Karls Universität TübingenTübingenGermany

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