Reconstructing orbit closures from their boundaries

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Families, moduli of curves (analytic) (14H15)

Cites Work

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Ergodicity of the absolute period foliation
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Full-rank affine invariant submanifolds
Rel leaves of the Arnoux-Yoccoz surfaces
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Minimal sets for flows on moduli space
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Rank 2 affine manifolds in genus \(3\)
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Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards
Translation surfaces and their orbit closures: an introduction for a broad audience
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The boundary of an affine invariant submanifold
\(\mathrm{GL}_2\mathbb{R}\) orbit closures in hyperelliptic components of strata
Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve
The field of definition of affine invariant submanifolds of the moduli space of abelian differentials
Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two
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Finiteness of Teichmüller Curves in Non-Arithmetic Rank 1 Orbit Closures
The WYSIWYG compactification
Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum ℋ(1,1)
Non-Existence and Finiteness Results for Teichmüller Curves in Prym Loci
Billiards, quadrilaterals and moduli spaces
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