scholarly journals Riemann Surface Structure for a Curved Surface with Punctured Features

2021 ◽  
Vol 2 (1) ◽  
pp. 7-16
Author(s):  
Ramya Deepak Shetty ◽  
Indira Narayana Swamy ◽  
Govind R Kadambi
Keyword(s):  
Riemann Surface ◽  
Surface Structure ◽  
Complex Plane ◽  
Stereographic Projection ◽  
Curved Surface ◽  
Triangular Meshes ◽  
Original Surface ◽  
Transition Functions ◽  
Rectangular Grids ◽  
Smooth Transitions

In this paper, a generic procedure for the development and subsequent validation of the Riemann surface structure (RSS) for a punctured curved surface lying on a Riemann surface is discussed. The proposed procedure differs from the existing methods involving triangular meshes and rectangular grids that rely on induced patches on surfaces. This procedure can be applied to non-punctured surfaces as well as to surfaces with irregularly located punctures. Further, by defining appropriate transition functions, the proposed procedure eliminates the requirement for smooth transitions across the boundaries of adjacent patches. The analytic formulations of the RSS for an ellipsoid and a sphere are elaborated using the proposed procedure. Moreover, the RSS of a sphere defined through a family of conformal unit discs is proven equivalent to that defined by an existing method based on stereographic projection. This study proves that a smooth projection between the surface and (a subset of) the complex plane  , can be remapped to the original surface.

scholarly journals MULTIVALUED FIELDS ON THE COMPLEX PLANE AND BRAID GROUP STATISTICS

1994 ◽  
Vol 09 (03) ◽  
pp. 313-325 ◽  
Author(s):  
FRANCO FERRARI
Keyword(s):  
Riemann Surface ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Conformal Field Theories ◽  
Local Exchange ◽  
R Matrix ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Nontrivial Topology

In this paper we study a class of theories of free particles on the complex plane satisfying a non-Abelian statistics. This kind of particles are generalizations of the anyons and are sometimes called plectons. The peculiarity of these theories is that they are associated to free conformal field theories defined on Riemann surfaces with a discrete and non-Abelian group of authomorphisms Dm. More explicitly, the plectons appear here as “induced vertex operators” that simulate, on the complex plane, the nontrivial topology of the Riemann surface. In order to express the local exchange algebra of the particles, one is led to introduce an R matrix satisfying a multiparameter generalization of the usual Yang-Baxter equations. It is interesting that analogous generalizations have already been investigated in connection with integrable models, in which the spectral parameter takes its values on a Riemann surface that is in many respects similar to the Riemann surfaces we are studying here. The explicit form of the R matrices mentioned above can be also used to define a multiparameter version of the quantum complex hyperplane.

scholarly journals Brain Surface Conformal Parameterization Using Riemann Surface Structure

2007 ◽  
Vol 26 (6) ◽  
pp. 853-865 ◽  
Author(s):  
Yalin Wang ◽  
Lok Ming Lui ◽  
Xianfeng Gu ◽  
Kiralee M. Hayashi ◽  
Tony F. Chan ◽  
...  
Keyword(s):  
Riemann Surface ◽  
Surface Structure ◽  
Brain Surface

scholarly journals Retinal vessel model fabricated on a curved surface structure for a simulation of microcannulation

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Takeshi Hayakawa ◽  
Ippei Kato ◽  
Fumihito Arai ◽  
Mamoru Mitsuishi ◽  
Naohiko Sugita ◽  
...  
Keyword(s):  
Surface Structure ◽  
Retinal Vessel ◽  
Curved Surface

scholarly journals Geometric Compression Using Riemann Surface Structure

2003 ◽  
Vol 3 (3) ◽  
pp. 171-182 ◽  
Author(s):  
Xianfeng Gu ◽  
Yalin Wang ◽  
Shing-Tung Yau
Keyword(s):  
Riemann Surface ◽  
Surface Structure

Qp Spaces on Riemann Surfaces

1998 ◽  
Vol 50 (3) ◽  
pp. 449-464 ◽  
Author(s):  
Rauno Aulaskari ◽  
Yuzan He ◽  
Juha Ristioja ◽  
Ruhan Zhao
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Hyperbolic Riemann Surfaces ◽  
Qp Spaces

AbstractWe study the function spaces Qp(R) defined on a Riemann surface R, which were earlier introduced in the unit disk of the complex plane. The nesting property Qp(R) ⊆Qq(R) for 0 < p < q < ∞ is shown in case of arbitrary hyperbolic Riemann surfaces. Further, it is proved that the classical Dirichlet space AD(R) ⊆ Qp(R) for any p, 0 < p < ∞, thus sharpening T. Metzger's well-known result AD(R) ⊆ BMOA(R). Also the first author's result AD(R) ⊆ VMOA(R) for a regular Riemann surface R is sharpened by showing that, in fact, AD(R) ⊆ Qp,0(R) for all p, 0 < p < ∞. The relationships between Qp(R) and various generalizations of the Bloch space on R are considered. Finally we show that Qp(R) is a Banach space for 0 < p < ∞.

1P1-E02 Fabrication of retinal vessel model with curved surface structure

2015 ◽  
Vol 2015 (0) ◽  
pp. _1P1-E02_1-_1P1-E02_4
Author(s):  
Fumihito ARAI ◽  
Ippei KATO ◽  
Mamoru MITSUISHI ◽  
Naohiko SUGITA ◽  
Kanako HARADA ◽  
...  
Keyword(s):  
Surface Structure ◽  
Retinal Vessel ◽  
Curved Surface

Great Circles and Rhumb Lines on the Complex Plane

2017 ◽  
Vol 70 (3) ◽  
pp. 618-627
Author(s):  
Robin G. Stuart
Keyword(s):  
Complex Plane ◽  
Stereographic Projection ◽  
Riemann Sphere ◽  
Complex Numbers ◽  
Spherical Trigonometry ◽  
Numerical Examples ◽  
Computer Evaluation

Mapping points on the Riemann sphere to points on the plane of complex numbers by stereographic projection has been shown to offer a number of advantages when applied to problems in navigation traditionally handled using spherical trigonometry. Here it is shown that the same approach can be used for problems involving great circles and/or rhumb lines and it results in simple, compact expressions suitable for efficient computer evaluation. Worked numerical examples are given and the values obtained are compared to standard references.

scholarly journals Brain Surface Parameterization Using Riemann Surface Structure

2005 ◽  
pp. 657-665 ◽  
Author(s):  
Yalin Wang ◽  
Xianfeng Gu ◽  
Kiralee M. Hayashi ◽  
Tony F. Chan ◽  
Paul M. Thompson ◽  
...  
Keyword(s):  
Riemann Surface ◽  
Surface Structure ◽  
Surface Parameterization ◽  
Brain Surface

A REMARK ON CONFORMAL FIELD THEORIES ON ALGEBRAIC CURVES

1991 ◽  
Vol 06 (12) ◽  
pp. 1103-1107 ◽  
Author(s):  
J. SOBCZYK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complex Plane ◽  
Algebraic Curves ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Branching Points ◽  
Branch Covering

We present an argument supporting the conjecture that a conformal field theory (CFT) defined on a Riemann surface viewed as a branch covering of CP 1 can be transformed to a CFT on the complex plane in which the information about branching points was coded into certain conformal field insertions.

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