A Sufficient Condition for Mi-groups

In this note, we give a sufficient condition for Mi-group. In particular, we show that if a finite group G is the semidirect product of two subgroups with coprime orders, in which one is a Sylow tower group and its Sylow subgroups are all abelian, and the other is an Mi-group and all of its proper subgroups are also Mi-groups, then G is an Mi-group.     

Convex hull of set in thick part of Teichmller space

Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n1.Let T(X)be the Teichmller space of X.By constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics.     

On the equivalence of extremal Teichmller mapping

Let T(△) and B(△) be the Teichmuller space and the infinitesimal Teichmuller space of the unit disk △ respectively. In this paper, we show that [ν]B(△) being an infinitesimal Strebel point does not imply that [ν]T(△) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved.     

Stable Teichmller mappings of type (0,4)

Let X = C{0,1} and X = X{}. We get a necessary and suficient condition on the position of  in X such that X has stable Teichmller mappings. Furthermore, we can formulate all these stable Teichmller mappings. The main result in this paper partially answers a question posed by Kra.     

A Necessary and Sufficient Condition for Admissibility of Nonnegative Quadratic Estimator

ＡＮｅｃｅｓｓａｒｙａｎｄＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎｆｏｒＡｄｍｉｓｓｉｂｉｌｉｔｙｏｆＮｏｎｎｅｇａｔｉｖｅＱｕａｄｒａｔｉｃＥｓｔｉｍａｔｏｒＬｕＣｈａｎｇｙｕ（鹿长余）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｏｒｔｈｅａ...     

A uniqueness property for the quantization of Teichmüller Spaces

Chekhov, Fock and Kashaev introduced a quantization of the Teichmüller space of a punctured surface S, and an exponential version of this construction was developed by Bonahon and Liu. The construction of crucially depends on certain coordinate change isomorphisms between the Chekhov–Fock algebras associated to different ideal triangulations of S. We show that these coordinate change isomorphisms are essentially unique, once we require them to satisfy a certain number of natural conditions.      

A Sufficient Condition for Interolation by Functions in A~P(φ) (1

肖杰  赵大蕻 《数学季刊》1992,(4)

Stability of quasi-geodesics in Teichmüller space

Let S be a surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that a Teichmüller quasi-geodesic in the thick part of Teichmüller space for S is contained in a bounded neighborhood of a geodesic if and only if it induces a quasi-geodesic in the curve graph.     

Teichmüller contraction in the Teichmüller space of a closed set in the sphere

We generalize the principle of Teichmüller contraction and deduce the Hamilton-Krushkaĺ condition for extremal quasiconformal mappings in the Teichmüller space of a closed set in the Riemann sphere.     

Asymptotics for Pseudo-Anosov Elements in Teichmüller Lattices

A Teichmüller lattice is the orbit of a point in Teichmüller space under the action of the mapping class group. We show that the proportion of lattice points in a ball of radius r which are not pseudo-Anosov tends to zero as r tends to infinity. In fact, we show that if R is a subset of the mapping class group, whose elements have an upper bound on their translation length on the complex of curves, then the proportion of lattice points in the ball of radius r which lie in R tends to zero as r tends to infinity.     

A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

ＡＮｅｃｅｓｓａｒｙａｎｄＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎＳａｔｉｓｆｉｅｄｂｙＤｅｃｏｍｐｏｓａｂｌｅＥｌｅｍｅｎｔｓｉｎＣｏｍｐｌｅｔｅｌｙＳｙｍｍｅｔｒｉｃａｌＴｅｎｓｏｒＳｐａｃｅｓ￥ＺｈｕＺｈｏｎｇｎａｎ（ＪｉａｎｇｓｕＥｄｕｃａｔｏ...     

A variational construction of the Teichmüller map

Gerstenhaber and Rauch proposed the problem of constructing the Teichmüller map by a maximum-minimum approach involving harmonic maps. In this paper, we show that the Teichmüller map can be constructed by this variational characterization. The key idea is to consider a class of metrics on the target which include singular metrics and use the harmonic map theory in this setting.Received: 29 June 2002, Accepted: 29 July 2003, Published online: 25 February 2004Chikako Mese: The author is supported by research grant NSF DMS #0072483 and the Woodrow Wilson National Fellowship Foundation. The author would like to thank the referee for his/her careful reading and helpful suggestions.     

Criteria for the divergence of pairs of Teichmüller geodesics

We study the asymptotic geometry of Teichmüller geodesic rays. We show that, when the transverse measures to the vertical foliations of the quadratic differentials determining two different rays are topologically equivalent, but are not absolutely continuous with respect to each other, the rays diverge in Teichmüller space.     

A Sufficient Condition for Splitting of Arithmetically Cohen–Macaulay Bundles on General Hypersurfaces

A vector bundle on a hypersurface is arithmetically Cohen–Macaulay if its intermediate cohomologies vanish. On projective spaces, such bundles coincide with those which split into a direct sum of line bundles, but this fails on hypersurfaces of higher degree in general. In this article, we give an inequality which gives a sufficient condition for splitting of arithmetically Cohen–Macaulay bundles on general hypersurfaces.     

A Necessary and Sufficient Condition for the Complete Reducibility of a g (A)-module

Suppose that A is an n×n complex matrix.The contragredient Lie algebraassociated to matrix A is denoted by g(A). A g(A)-module V is called h-diagonalizable if it admits a weight space decom-position V= V_λ,and dimV_λ<∞. Let P(V)={λ∈h外\*|V_λ≠0} be the set of weightsof V.For λ∈h*,set D(λ)={μ∈h*|μ≤λ}.     

A binary infinitesimal form of the Teichmüller metric

Let S be a hyperbolic Riemann surface of finite analytic type. We give a binary infinitesimal form of the Teichmüllermetric on the Teichmüller space T(S) of S by use of the fundamental Reich-Strebel inequalities. As an application, we reduce the Teichmüller disk problem to the infinitesimal setting. Moreover, we define the “angle” between geodesic rays in T(S) and give an explicit formula.     

Teichmller space of negatively curved metrics on complex hyperbolic manifolds is not contractible

We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T0(M)). T0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.     

Sufficient and Necessary Condition for the Measurability of Fallable Fuzzy Sets

Let(X,)be a measurable space,and,=σ-field generated by {x|x∈X},where x={A∈ |x∈A}.(Y,)another measurable space,let ρ(X, Y,)={∈ |§ be measurable}.∈ρ(X,Y,),we define ()(y)=~(-1)(y),y∈y. Defination 1.T is an index set,f:{0,1}~T→{0,1},then,O~T:( (Y)~x)~T→ (Y)~x is called the operation derived from f if for any { }_(t∈T)∈((Y)~x)~Tand any(x,y)∈X×Y,it holds