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arXiv · 1508.01446

The boundary of an affine invariant submanifold

Maryam Mirzakhani·Alex Wright
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Abstract

We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.

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Maryam Mirzakhani, Alex Wright. 2015-08-06. The boundary of an affine invariant submanifold. https://arxiv.org/abs/1508.01446

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