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The boundary of an affine invariant submanifold

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.

preprint2020arXivOpen access
Maryam MirzakhaniAlex Wright
math.DSmath.GT
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Maryam MirzakhaniAlex Wright

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