On long complex projective tubes, the Schwarzian derivative is asymptotically (1/2z^2)(1+4π^2/ℓ^2) dz^2 up to exponentially small errors, giving control of renormalized volume under earthquakes and grafting.
Schwarzian derivatives, projective structures, and the W eil- P etersson gradient flow for renormalized volume
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Behaviour of the Schwarzian derivative on long complex projective tubes
On long complex projective tubes, the Schwarzian derivative is asymptotically (1/2z^2)(1+4π^2/ℓ^2) dz^2 up to exponentially small errors, giving control of renormalized volume under earthquakes and grafting.