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arXiv · 1808.03456

The Helfrich Boundary Value Problem

Sascha Eichmann
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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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Sascha Eichmann. 2018-08-10. The Helfrich Boundary Value Problem. https://doi.org/10.1007/s00526-018-1468-x

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