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Introduction to Teichmu¨ller Theory - UC Davis
www.math.ucdavis.edu12 Teichm ̈uller theory from the Kodaira-Spencer point of view. Definition (Kodaira- Spencer): A holomorphic family is a complex manifold V = V m+1 and a holomorphic map π : V → M = Mm where Mm is a complex manifold and all preimages π−1(t) are Riemann surfaces (t M). In our case, M = Φ(T (X)) ⊂ Q(X) and ∈.
Teichmu¨ller Theory Notes - Harvard University
people.math.harvard.eduThe 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.