Abstract
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 Gro{\ss}e-Brauckmann.
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