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arXiv · 2008.06625

The space of partially free boundary minimal half disks

Shanjiang Chen
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Abstract

This paper forms part of our ongoing works on the existence of complete non-compact free boundary minimal planes in an asymptotically flat three-dimensional Riemannian manifold with boundary. We set up the degree theory for the space of properly embedded partially free boundary minimal half disks in a three-dimensional half ball. We prove that the space of such surfaces is a Banach manifold. The projection map which projects partially free boundary minimal half disks into their Dirichlet boundaries is a Fredholm map of index zero and has a well-defined mod-2 degree under suitable assumptions. The new major analytic difficulty is to analyze the properties of a second order elliptic operator with mix boundary conditions on a domain with corners.

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Shanjiang Chen. 2020-10-10. The space of partially free boundary minimal half disks. https://arxiv.org/abs/2008.06625

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