共查询到20条相似文献,搜索用时 15 毫秒
1.
The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37π2/1080 in the metric of constant curvature ?1. Each of the five connected components of the moduli space can be described as the quotient of real hyperbolic four-space by a specific arithmetic group. We compute the volumes of these components. To cite this article: D. Allcock et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
2.
Tatyana Foth 《Differential Geometry and its Applications》2008,26(1):63-74
Let X be CPn or a compact smooth quotient of the n-dimensional complex hyperbolic space, n>1. Let L be a hermitian holomorphic line bundle (with hermitian connection) on X chosen as follows: if X=CPn then L is the hyperplane bundle, and in the second case L is chosen so that L⊗(n+1)=KX⊗E, where KX is the canonical line bundle and E is a flat line bundle. The unit circle bundle P in L∗ is a contact manifold. Let k′ be a fixed positive integer. We construct certain Legendrian tori in P (the construction depends, in particular, on the choice of k′) and sequences {uk}, k=k′m, , of holomorphic sections of L⊗k associated to these tori. We study asymptotics of the norms ‖ukk‖ as m→+∞ and, in particular, apply this result to construct explicitly certain non-trivial holomorphic automorphic forms on the n-dimensional complex hyperbolic space. We obtain an n>1 analogue of the classical period formula (this is a well-known statement for automorphic forms on the upper half plane, n=1). 相似文献
3.
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88-91] and the second author [P. Tumarkin, Compact hyperbolic Coxeter n-polytopes with n+3 facets, Electron. J. Combin. 14 (2007), R69, 36 pp.], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and in dimension 8. 相似文献
4.
We introduce a concept of independence entropy for symbolic dynamical systems. This notion of entropy measures the extent to which one can freely insert symbols in positions without violating the constraint defined by the shift space. We show that for a certain class of one-dimensional shift spaces X, the independence entropy coincides with the limiting, as d tends to infinity, topological entropy of the dimensional shift defined by imposing the constraints of X in each of the d cardinal directions. This is of interest because for these shift spaces independence entropy is easy to compute. Thus, while in these cases, the topological entropy of the d-dimensional shift (d≥2) is difficult to compute, the limiting topological entropy is easy to compute. In some cases, we also compute the rate of convergence of the sequence of d-dimensional entropies. This work generalizes earlier work on constrained systems with unconstrained positions. 相似文献
5.
Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X/G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn-Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g∈G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the first named author in a number of ways. 相似文献
6.
Boris Rubin 《Advances in Mathematics》2002,170(2):206-223
New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms. 相似文献
7.
Jaume Llibre 《Journal of Differential Equations》1984,54(2):221-230
It is shown that the n-body problem in a d-dimensional space has no C1-extendable regular integrals if n ? d + 1. 相似文献
8.
《Journal of Functional Analysis》1987,75(1):161-187
Using techniques of stationary scattering theory for the Schrödinger equation, we show absence of singular spectrum and obtain incoming and outgoing spectral representations for the Laplace-Beltrami operator on manifolds Mn arising as the quotient of hyperbolic n-dimensional space by a geometrically finite, discrete group of hyperbolic isometries. We consider manifolds Mn of infinite volume. In subsequent papers, we will use the techniques developed here to analytically continue Eisenstein series for a large class of discrete groups, including some groups with parabolic elements. 相似文献
9.
Zonglao Zhang 《Journal of Mathematical Analysis and Applications》2005,305(2):491-501
In this paper we investigate the mean curvature H of a radial graph in hyperbolic space Hn+1. We obtain an integral inequality for H, and find that the lower limit of H at infinity is less than or equal to 1 and the upper limit of H at infinity is more than or equal to −1. As a byproduct we get a relation between the n-dimensional volume of a bounded domain in an n-dimensional hyperbolic space and the (n−1)-dimensional volume of its boundary. We also sharpen the main result of a paper by P.-A. Nitsche dealing with the existence and uniqueness of graph-like prescribed mean curvature hypersurfaces in hyperbolic space. 相似文献
10.
11.
Given a substitution σ ond letters, we define itsk-dimensional extension,E
k (σ), for 0≤k≤d. Thek-dimensional extension acts on the set ofk-dimensional faces of unit cubes inR
d with integer vertices. The extensions of a substitution satisfy a commutation relation with the natural boundary operator:
the boundary of the image is the image of the boundary. We say that a substitution is unimodular (resp. hyperbolic) if the
matrix associated to the substitution by abelianization is unimodular (resp. hyperbolic). In the case where the substitution
is unimodular, we also define dual substitutions which satisfy a similar coboundary condition. We use these constructions
to build self-similar sets on the expanding and contracting space for an hyperbolic substitution. 相似文献
12.
We prove that the kernel of a quotient operator from an L 1-space onto a Banach space X with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky-case ? 1-and Figiel, Johnson and Pe?czyński-case X* separable. Given a Banach space X, we show that if the kernel of a quotient map from some L 1-space onto X has the BAP, then every kernel of every quotient map from any L 1-space onto X has the BAP. The dual result for L ∞-spaces also holds: if for some L ∞-space E some quotient E/X has the BAP, then for every L ∞-space E every quotient E/X has the BAP. 相似文献
13.
Simon Marshall 《Israel Journal of Mathematics》2014,200(1):423-448
Let Y be an arithmetic hyperbolic 3-manifold. We establish a link between quantum unique ergodicity for sections of automorphic vector bundles on Y and subconvexity for the triple product L-function, which extends a result of Watson in the case of hyperbolic 2-manifolds. The proof combines the representation theoretic microlocal lift for bundles developed by Bunke and Olbrich with the triple product formula of Ichino. A key step is determining the asymptotic behaviour of the local integrals at complex places that appear in Ichino’s formula. 相似文献
14.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(1):105-110
We give a fast algorithm to evaluate a class of d-dimensional integrals. A direct numerical evaluation of these integrals costs Nd, where d is the number of variables and N is the number of discrete points of each variable. The algorithm we present in this Note permits to reduce this cost from Nd to a cost of the order O(N). This recursive algorithm takes its inspiration from the well-known Fast-Multipole method. At the end of this paper we give some physical applications of such an algorithm. 相似文献
15.
Let Γ be an arithmetic group of affine automorphisms of the n-dimensional future tube T. It is proved that the quotient space T/Γ is smooth at infinity if and only if the group Γ is generated by reflections and the fundamental polyhedral cone (“Weyl chamber”) of the group dΓ in the future cone is a simplicial cone (which is possible only for n ≤ 10). As a consequence of this result, a smoothness criterion for the Satake–Baily–Borel compactification of an arithmetic quotient of a symmetric domain of type IV is obtained. 相似文献
16.
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $\bar X \to X$ of X as a quotient of a vector space $\bar X$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation. 相似文献
17.
Walter Benz 《Journal of Geometry》2009,93(1-2):28-33
Let X be a real inner product space of (finite or infinite) dimension greater than one. We proved (see Theorem 7, Chapter 1 of our book [1]) that if T is a separable translation group of X, and d an appropriate distance function of X which is supposed to be invariant under T and the orthogonal group O of X, then there are, up to isomorphism, exactly two solutions of geometries (X,G(T,O)), G the group generated by T ∪ O, namely euclidean and hyperbolic geometry over X. With the same geometrical definition for both geometries of arbitrary (finite or infinite) dimension > 1 we will characterize in this note the notion of orthogonality. 相似文献
18.
Petr Hájek 《Journal of Differential Equations》2010,249(12):3342-3351
We show that if X is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping f:X→X such that the autonomous differential equation x′=f(x) has no solution at any point. 相似文献
19.
We develop a global Poincaré residue formula to study period integrals of families of complex manifolds. For any compact complex manifold X equipped with a linear system V ? of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on X. Two important ingredients of this construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize the construction to CY and general type complete intersections. When X is an algebraic manifold having a sufficiently large automorphism group G and V ? is a linear representation of G, we construct a holonomic D-module that governs the period integrals. The construction is based in part on the theory of tautological systems we have developed in the paper Lian, Song and Yau (arXiv:1105.2984v1, 2011). The approach allows us to explicitly describe a Picard-Fuchs type system for complete intersection varieties of general types, as well as CY, in any Fano variety, and in a homogeneous space in particular. In addition, the approach provides a new perspective of old examples such as CY complete intersections in a toric variety or partial flag variety. 相似文献
20.
We can describe higher-dimensional classical spaces by analytical projective geometry, if we embed the d-dimensional real space onto a d + 1-dimensional real projective metric vector space. This method allows an approach to Euclidean, hyperbolic, spherical and
other geometries uniformly [8].
To visualize d-dimensional solids, it is customary to make axonometric projection of them. In our opinion the central projection gives more
information about these objects, and it contains the axonometric projection as well, if the central figure is an ideal point
or an s-dimensional subspace at infinity. We suggest a general method which can project solids into any picture plane (space) from
any central figure, complementary to the projection plane (space). Opposite to most of the other algorithms in the literature,
our algorithm projects higher-dimensional solids directly into the two-dimensional picture plane (especially into the computer
screen), it does not use the three-dimensional space for intermediate step.
Our algorithm provides a general, so-called lexicographic visibility criterion in Definition and Theorem 3.4, so it determines
an extended visibility of the d-dimensional solids by describing the edge framework of the two-dimensional surface in front of us. In addition we can move
the central figure and the image plane of the projection, so we can simulate the moving position of the observer at fixed
objects on the computer screen (see first our figures in reverse order).
Supported by DAAD 2008 Multimedia Technology for Mathematics and Computer Science Education. 相似文献