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arXiv · 1906.05720

Reflection of Willmore surfaces with free boundaries

Ernst Kuwert·Tobias Lamm
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Abstract

We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

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Ernst Kuwert, Tobias Lamm. 2019-06-13. Reflection of Willmore surfaces with free boundaries. https://doi.org/10.4153/s0008414x20000164

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