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Teichmu¨ller Theory Notes - Harvard University

The integral geometric measure on G is defined as follows. Fix an oriented geodesic γ ⊂ H. Then there is an injective map (x, θ) to the unique unoriented geodesic δ(x, θ) through γ × S1 → G sending. x making angle θ with γ. (Since the geodesics are unoriented, θ ranges in [0, π].) The measure = (1/2) sin θdθ dx.

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