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51.
This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants. 相似文献
52.
By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation. 相似文献
53.
We consider a period map from Teichmüller space to
, which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle
and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP
g
() by the group
. 相似文献
54.
黄倩霞 《广西师范学院学报(自然科学版)》1998,(4)
该文引入了一类包含S-闭空间的拓扑空间——WS*-闭空间,并讨论了它的一些性质,对一些关于S-闭空间的已知命题,建立或推广得到WS*-闭空间的相应命题。 相似文献
55.
Bernd Siebert 《Mathematische Annalen》1993,296(1):269-283
This and the second part of the paper are to a great extent parts of my thesis [Si] which also appeared as preprint Mathematica Gottingensis 5/92. This work was partly supported by the S7B170 Geometrie und Analysis in Göttingen 相似文献
56.
Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant 总被引:1,自引:0,他引:1
Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of
d
. Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship 相似文献
57.
Ming Liao 《Probability Theory and Related Fields》1993,96(2):261-281
Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS
n–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS
n–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China 相似文献
58.
We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current.
We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give
some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex
manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the
intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive
when the intersection of their singular supports is contained in a Stein domain.
The first author was partially supported by National Science Foundation Grant Nos. DMS-8922760 and DMS-9204273. The second
author was partially supported by National Science Foundation Grant Nos. DMS-9001365 and DMS-9204037. 相似文献
59.
In this paper we prove local analyticity of solutions to the
-Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These
are domains that are locally of the form Imw > Σ |h
k
(z
k
)|2 with eachh
k
holomorphic and vanishing only at 0.
As in those earlier papers, we use purelyL
2 methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew. 相似文献
60.
Steven Bell 《Journal of Geometric Analysis》1993,3(3):195-224
We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz
0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported
away fromz
0 cannot vanish to infinite order atz
0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the
problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in
several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection
and kernel in planar domains.
Research supported by NSF Grant DMS-8922810. 相似文献