For every genus, any SL2(R)-orbit in the moduli space of flat surfaces whose stabilizer is not a lattice has critical exponent at most 1 - ε_g, a uniform gap.
Symplectic and isometric SL2(R)-invariant sub- bundles of the Hodge bundle
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Orbits in Teichm\"uller dynamics admits a critical exponent gap
For every genus, any SL2(R)-orbit in the moduli space of flat surfaces whose stabilizer is not a lattice has critical exponent at most 1 - ε_g, a uniform gap.