Measured foliations and harmonic maps of surfaces
نویسندگان
چکیده
منابع مشابه
Measured Foliations and Harmonic Maps of Surfaces
Fix a Riemannian surface of negative curvature (N, h), and a differentiable surface M g of the same genus g that will host various structures. Also fix a diffeomorphism f0 : M → N . It is well known ([ES], [A], [SY1], [Sa]) that to every complex structure σ on M , there is a unique harmonic diffeomorphism f(σ) : M(σ) → (N, h) homotopic to f0 : M → N ; one is led to consider what other, possibly...
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We give a brief, elementary and analytic proof of the theorem of Hubbard and Masur [HM] (see also [K], [G]) that every class of measured foliations on a compact Riemann surface R of genus g can be uniquely represented by the vertical measured foliation of a holomorphic quadratic differential on R. The theorem of Thurston [Th] that the space of classes of projective measured foliations is a 6g −...
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We prove a rigidity result on the action of the extended mapping class group Γ∗(S) of a closed surface S of genus ≥ 2 on Thurston’s space of measured foliations MF(S). More precisely, we describe a natural homomorphism from Γ∗(S) to the automorphism group of the train track PL structure of MF(S) and we prove that if the genus of S is ≥ 3, then this natural homomorphism is an isomorphism, and if...
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Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1998
ISSN: 0022-040X
DOI: 10.4310/jdg/1214461107