29,961 research outputs found
Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space
We give an effective estimate for the totally ramified value number of the
hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As
a corollary, we give the upper bound of the number of exceptional values of
them for some topological cases. Moreover, we obtain some new examples for this
class.Comment: 14 pages, to appear in Houston Journal of Mathematic
Anyon Basis of c=1 Conformal Field Theory
We study the conformal field theory of a free compactified boson with
radius ( is an integer). The Fock space of this boson
is constructed in terms of anyon vertex operators and each state is labeled by
an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave
function of multi anyon state is described by an eigenfunction of the
Calogero-Sutherland (CS) model. The conformal field theory at
gives a field theory of CS model. This is a natural
generalization of the boson-fermion correspondence in one dimension to
boson-anyon correspondence. There is also an interesting duality between anyon
with statistics and particle with statistics .Comment: 17 page
Function-theoretic properties for the Gauss maps of various classes of surfaces
We elucidate the geometric background of function-theoretic properties for
the Gauss maps of several classes of immersed surfaces in three-dimensional
space forms, for example, minimal surfaces in Euclidean three-space, improper
affine spheres in the affine three-space, and constant mean curvature one
surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose,
we prove an optimal curvature bound for a specified conformal metric on an open
Riemann surface and give some applications. We also provide unicity theorems
for the Gauss maps of these classes of surfaces.Comment: 26 pages. arXiv admin note: substantial text overlap with
arXiv:1205.478
Ramification estimates for the hyperbolic Gauss map
We give the best possible upper bound on the number of exceptional values and
the totally ramified value number of the hyperbolic Gauss map for
pseudo-algebraic constant mean curvature one surfaces in the hyperbolic
three-space and some partial results on the Osserman problem for algebraic
case. Moreover, we study the value distribution of the hyperbolic Gauss map for
complete constant mean curvature one faces in de Sitter three-space.Comment: 16 pages, corrected some typos. OCAMI Preprint Series 08-1, to appear
in Osaka Journal of Mathematic
Four-Dimensional Painlev\'e-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems
This is the last part of a series of three papers entitled "Four-dimensional
Painlev\'e-type equations associated with ramified linear equations". In this
series of papers we aim to construct the complete degeneration scheme of
four-dimensional Painlev\'e-type equations. In the present paper, we consider
the degeneration of the Garnier system in two variables and the Fuji-Suzuki
system
On the maximal number of exceptional values of Gauss maps for various classes of surfaces
The main goal of this paper is to reveal the geometric meaning of the maximal
number of exceptional values of Gauss maps for several classes of immersed
surfaces in space forms, for example, complete minimal surfaces in the
Euclidean three-space, weakly complete improper affine spheres in the affine
three-space and weakly complete flat surfaces in the hyperbolic three-space.
For this purpose, we give an effective curvature bound for a specified
conformal metric on an open Riemann surface.Comment: 13 pages, to appear in Mathematische Zeitschrif
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