Ray structures on teichmüller space
WebTheorem 2.11. Let (l1,l2,l3) ∈ R3 be nonnegative numbers. Then there exists a complete hyperbolic structure X with geodesic boundary on the pair of pants (S2 \ 3 discs) such … WebWe first depict harmonic map ray structures on Teichmüller space as a geometric transition between Teichmüller ray structures and Thurston geodesic ray structures. In particular, …
Ray structures on teichmüller space
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WebAug 1, 2016 · Here, ML is the space of measured laminations on the surface, ℓ λ: T g, n → R is the geodesic length function on Teichmüller space associated to the measured lamination λ and d ℓ λ is the differential of ℓ λ at the point X ∈ T g, n. There is a (non-necessary unique) extremal Lipschitz homeomorphism that realizes the infimum in (6). WebThe Complex Structure of the Teichmüller Space 479 The symmetric form Re θAθ¯ B(Imz)2 equals s(A,B)= 2 π δA,BLA + A\ / B c log c+1 c−1 −2. (2.7) Here c =cosθp at each intersection point of α ·β or c =coshδ, where δ is the hyperbolic distance from the axis of A to each disjoint axis congruent to the axis of B. (δA,B is the Kronecker symbol equal to 1 if A=B …
WebDec 6, 2012 · This book offers an easy and compact access to the theory of Teichmüller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichmüller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is … WebThe Teichmüller space T is the space of conformal structures on S up to conformal automorphisms which are isotopic to the identity. By the uniformization theorem, we may …
WebRay structures on Teichmüller Space While there may be many Thurston metric geodesics between a pair of points in Teichm\"uller space, we find that by imposing an additional … WebAug 21, 2010 · We prove, however, that the quotient of the augmented Teichmüller space by any finite index subgroup of the Teichmüller modular group has a canonical structure of a complex orbifold. Using this structure, we construct natural maps from {\overline {\mathcal {T}}} to stacks of admissible coverings of stable Riemann surfaces.
WebNov 17, 2011 · Download PDF Abstract: We highlight several analogies between the Finsler (infinitesimal) properties of Teichmüller's metric and Thurston's asymmetric metric on Teichmüller space. Thurston defined his asymmetric metric in analogy with Teichmüllers' metric, as a solution to an extremal problem, which consists, in the case of the …
WebThe Teichmüller space has a canonical complex manifold structure and a wealth of natural metrics. The study of geometric features of these various structures is an active body of … how many quarts in a gallon oilhow dbms_scheduler works in oracleWebJan 7, 2024 · structure and ς is a quadratic differential, then there exists a projective structure β such that a - β = q. Moreover, (a - β) + (β - η) = a - η. This all follows from … how dbt helps with emotionsWebJ. DIFFERENTIAL GEOMETRY 35(1992) 151-217 HARMONIC MAPS, LENGTH, AND ENERGY IN TEICHMULLER SPACE YAIR N. MINSKY Abstract The limiting behavior of high-energy … how many quarts in one peckWebApr 11, 2024 · Huiping PAN 潘会平 (South China University of Technology 华南理工大学), 2024-10-24, Ray structures on Teichmüller space. Teichmüller space admits several ray … how dc to ac converter worksWebJun 2, 2024 · Furthermore, the conformal structure on that parallelogram descends to a conformal structure on the glued up torus (because the four vertices of the parallelogram … how dc-dc converter worksWeba consequence the projection of a generic grafting ray to the moduli space is dense. We also show that the set of points in Teichmüller space obtained by integer (2ˇ–) graftings on … how many quarts in a year