Displaying similar documents to “Computing the determinantal representations of hyperbolic forms”

Hyperbolic spaces in Teichmüller spaces

Christopher J. Leininger, Saul Schleimer (2014)

Journal of the European Mathematical Society

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We prove, for any n , that there is a closed connected orientable surface S so that the hyperbolic space n almost-isometrically embeds into the Teichmüller space of S , with quasi-convex image lying in the thick part. As a consequence, n quasi-isometrically embeds in the curve complex of S .

Hyperideal polyhedra in hyperbolic 3-space

Xiliang Bao, Francis Bonahon (2002)

Bulletin de la Société Mathématique de France

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A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic 3 -space 3 which, in the projective model for 3 ℝℙ 3 , is just the intersection of 3 with a projective polyhedron whose vertices are all outside 3 and whose edges all meet 3 . We classify hyperideal polyhedra, up to isometries of 3 , in terms of their combinatorial type and of their dihedral angles.

A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series

Mordechay B. Levin (2013)

Colloquium Mathematicae

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We prove the central limit theorem for the multisequence 1 n N 1 n d N d a n , . . . , n d c o s ( 2 π m , A n . . . A d n d x ) where m s , a n , . . . , n d are reals, A , . . . , A d are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in [ 0 , 1 ] s . The main tool is the S-unit theorem.

The existence of Carathéodory solutions of hyperbolic functional differential equations

Adrian Karpowicz (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider the following Darboux problem for the functional differential equation ² u / x y ( x , y ) = f ( x , y , u ( x , y ) , u / x ( x , y ) , u / y ( x , y ) ) a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b] 0 , a ] × ( 0 , b ] , where the function u ( x , y ) : [ - a , 0 ] × [ - b , 0 ] k is defined by u ( x , y ) ( s , t ) = u ( s + x , t + y ) for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.

Effective bounds for Faltings’s delta function

Jay Jorgenson, Jürg Kramer (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces X , nowadays called Faltings’s delta function and here denoted by δ Fal ( X ) . For a given compact Riemann surface X of genus g X = g , the invariant δ Fal ( X ) is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space g of genus g curves determined by X to its boundary g . In this paper we begin by revisiting a formula derived...

Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot, Marc Peigné (2006)

Bulletin de la Société Mathématique de France

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We consider a large class of non compact hyperbolic manifolds M = n / Γ with cusps and we prove that the winding process ( Y t ) generated by a closed 1 -form supported on a neighborhood of a cusp 𝒞 , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp 𝒞 and the Poincaré exponent δ of Γ . No assumption on the value of δ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez. ...

Hyperbolic measure of maximal entropy for generic rational maps of k

Gabriel Vigny (2014)

Annales de l’institut Fourier

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Let f be a dominant rational map of k such that there exists s < k with λ s ( f ) > λ l ( f ) for all l . Under mild hypotheses, we show that, for A outside a pluripolar set of Aut ( k ) , the map f A admits a hyperbolic measure of maximal entropy log λ s ( f ) with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of f to k + 1 . This provides many examples where non uniform hyperbolic dynamics is established. One of the key tools is to approximate...

Nonexistence results for the Cauchy problem of some systems of hyperbolic equations

Mokhtar Kirane, Salim Messaoudi (2002)

Annales Polonici Mathematici

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We consider the systems of hyperbolic equations ⎧ u = Δ ( a ( t , x ) u ) + Δ ( b ( t , x ) v ) + h ( t , x ) | v | p , t > 0, x N , (S1) ⎨ ⎩ v = Δ ( c ( t , x ) v ) + k ( t , x ) | u | q , t > 0, x N u = Δ ( a ( t , x ) u ) + h ( t , x ) | v | p , t > 0, x N , (S2) ⎨ ⎩ v = Δ ( c ( t , x ) v ) + l ( t , x ) | v | m + k ( t , x ) | u | q , t > 0, x N , (S3) ⎧ u = Δ ( a ( t , x ) u ) + Δ ( b ( t , x ) v ) + h ( t , x ) | u | p , t > 0, x N , ⎨ ⎩ v = Δ ( c ( t , x ) v ) + k ( t , x ) | v | q , t > 0, x N , in ( 0 , ) × N with u(0,x) = u₀(x), v(0,x) = v₀(x), uₜ(0,x) = u₁(x), vₜ(0,x) = v₁(x). We show that, in each case, there exists a bound B on N such that for 1 ≤ N ≤ B solutions to the systems blow up in finite time.

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung (2014)

Journal of the European Mathematical Society

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Let Y be a hyperbolic surface and let φ be a Laplacian eigenfunction having eigenvalue - 1 / 4 - τ 2 with τ > 0 . Let N ( φ ) be the set of nodal lines of φ . For a fixed analytic curve γ of finite length, we study the number of intersections between N ( φ ) and γ in terms of τ . When Y is compact and γ a geodesic circle, or when Y has finite volume and γ is a closed horocycle, we prove that γ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between N ( φ ) and γ is O ( τ ) . This bound is...

C 1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Jaume Llibre, Víctor F. Sirvent (2016)

Mathematica Bohemica

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Let X be a connected closed manifold and f a self-map on X . We say that f is almost quasi-unipotent if every eigenvalue λ of the map f * k (the induced map on the k -th homology group of X ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f * k with k odd is equal to the sum of the multiplicities of λ as eigenvalue of all the maps f * k with k even. We prove that if f is C 1 having finitely many periodic points all of them...

Nonconventional limit theorems in averaging

Yuri Kifer (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider “nonconventional” averaging setup in the form d X ε ( t ) d t = ε B ( X ε ( t ) , 𝛯 ( q 1 ( t ) ) , 𝛯 ( q 2 ( t ) ) , ... , 𝛯 ( q ( t ) ) ) where 𝛯 ( t ) , t 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while q j ( t ) = α j t , α 1 l t ; α 2 l t ; l t ; α k and q j , j = k + 1 , ... , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.

Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives

Adrian Karpowicz (2008)

Annales Polonici Mathematici

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We consider the Darboux problem for a functional differential equation: ( ² u ) / ( x y ) ( x , y ) = f ( x , y , u ( x , y ) , u ( x , y ) , u / x ( x , y ) , u / y ( x , y ) ) a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]∖(0,a]×(0,b], where the function u ( x , y ) : [ - a , 0 ] × [ - b , 0 ] k is defined by u ( x , y ) ( s , t ) = u ( s + x , t + y ) for (s,t) ∈ [-a₀,0]×[-b₀,0]. We give a few theorems about weak and strong inequalities for this problem. We also discuss the case where the right-hand side of the differential equation is linear.

An arithmetic Riemann-Roch theorem for pointed stable curves

Gérard Freixas Montplet (2009)

Annales scientifiques de l'École Normale Supérieure

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Let ( 𝒪 , Σ , F ) be an arithmetic ring of Krull dimension at most 1, 𝒮 = Spec 𝒪 and ( π : 𝒳 𝒮 ; σ 1 , ... , σ n ) an n -pointed stable curve of genus g . Write 𝒰 = 𝒳 j σ j ( 𝒮 ) . The invertible sheaf ω 𝒳 / 𝒮 ( σ 1 + + σ n ) inherits a hermitian structure · hyp from the dual of the hyperbolic metric on the Riemann surface 𝒰 . In this article we prove an arithmetic Riemann-Roch type theorem that computes the arithmetic self-intersection of ω 𝒳 / 𝒮 ( σ 1 + ... + σ n ) hyp . The theorem is applied to modular curves X ( Γ ) , Γ = Γ 0 ( p ) or Γ 1 ( p ) , p 11 prime, with sections given by the cusps. We show Z ' ( Y ( Γ ) , 1 ) e a π b Γ 2 ( 1 / 2 ) c L ( 0 , Γ ) , with p 11 m o d 12 when Γ = Γ 0 ( p ) . Here Z ( Y ( Γ ) , s ) is the Selberg...

Pointed k -surfaces

Graham Smith (2006)

Bulletin de la Société Mathématique de France

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Let S be a Riemann surface. Let 3 be the 3 -dimensional hyperbolic space and let 3 be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping ϕ : S 3 = ^ . If i : S 3 is a convex immersion, and if N is its exterior normal vector field, we define the Gauss lifting, ı ^ , of i by ı ^ = N . Let n : U 3 3 be the Gauss-Minkowski mapping. A solution to the Plateau problem ( S , ϕ ) is a convex immersion i of constant Gaussian curvature equal to k ( 0 , 1 ) such that the Gauss lifting ( S , ı ^ ) is complete and n ı ^ = ϕ . In this...

Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds

David Borthwick, Colin Guillarmou (2016)

Journal of the European Mathematical Society

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On geometrically finite hyperbolic manifolds Γ d , including those with non-maximal rank cusps, we give upper bounds on the number N ( R ) of resonances of the Laplacian in disks of size R as R . In particular, if the parabolic subgroups of Γ satisfy a certain Diophantine condition, the bound is N ( R ) = 𝒪 ( R d ( log R ) d + 1 ) .

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dibakar Dey, Pradip Majhi (2021)

Communications in Mathematics

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The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a ( k , μ ) -almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) . Also in ( k , μ ) -almost Kenmotsu manifolds the following conditions: (1) local symmetry ( R = 0 ) , (2) semisymmetry ( R · R = 0 ) , (3) Q ( S , R ) = 0 , (4) R · R = Q ( S , R ) , (5) locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) are equivalent. Further, it is proved that a ( k , μ ) ' -almost Kenmotsu manifold...