scholarly journals A Theorem on an Analytic Mapping of Riemann Surfaces

1961 ◽  
Vol 19 ◽  
pp. 149-157
Author(s):  
Minoru Kurita
Keyword(s):  
Differential Geometry ◽  
Riemann Surfaces ◽  
View Point ◽  
Analytic Mapping ◽  
Circular Points ◽  
Analytic Mappings

Recently S. S. Chern [1] intended an aproach to some problems about analytic mappings of Riemann surfaces from a view-point of differential geometry. In that line we treat here orders of circular points of analytic mappings. The author expresses his thanks to Prof. K. Noshiro for his kind advices.

scholarly journals The Riemann surface of a ring

1969 ◽  
Vol 10 (1-2) ◽  
pp. 251-256
Author(s):  
M. G. Stanley
Keyword(s):  
Riemann Surface ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Contravariant Functor ◽  
Trivial Representation ◽  
Analytic Mapping ◽  
Algebra Of Functions ◽  
The Right ◽  
Analytic Mappings

The contravariant functor F from the category of Riemann surfaces and analytic mappings to the category of complex algebras and homomorphisms which takes each surface Ω to the algebra of analytic functions on Ω does not have an adjoint on the right; but it nearly does. To each algebra A there is associated a surface Σ1 (A) and a homomorphism A from A into FΣ1 (A), indeed onto an algebra of functions not all of which are constant on any component of Σ1 (A), such that every such non-trivial representation A A → F(Ω) is induced by a unique analytic mapping Ω → Σ1(A)

scholarly journals Generic affine differential geometry of plane curves

1998 ◽  
Vol 41 (2) ◽  
pp. 315-324 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Takasi Sano
Keyword(s):  
Differential Geometry ◽  
Singularity Theory ◽  
Affine Differential Geometry ◽  
Plane Curves ◽  
View Point ◽  
Smooth Functions ◽  
Affine Invariants

We study affine invariants of plane curves from the view point of the singularity theory of smooth functions

On analytic mappings of Riemann surfaces

1959 ◽  
Vol 7 (1) ◽  
pp. 249-279 ◽  
Author(s):  
H. J. Landau ◽  
R. Osserman
Keyword(s):  
Riemann Surfaces ◽  
Analytic Mappings

scholarly journals Finite Determinacy and Stability of Flatness of Analytic Mappings

2017 ◽  
Vol 69 (02) ◽  
pp. 241-257
Author(s):  
Janusz Adamus ◽  
Hadi Seyedinejad
Keyword(s):  
Complete Intersection ◽  
Complete Intersections ◽  
Finite Determinacy ◽  
Analytic Mapping ◽  
Analytic Mappings

Abstract It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of complete intersections. It is also shown that flatness and openness are stable under deformations.

Registration of Point Clouds Based on Differential Geometry of Surface’s Feature

2011 ◽  
Vol 101-102 ◽  
pp. 232-235
Author(s):  
Xue Сhang Zhang ◽  
Xue Jun Gao
Keyword(s):  
Differential Geometry ◽  
Point Cloud ◽  
Optimal Algorithm ◽  
Point Clouds ◽  
View Point ◽  
Geometric Information ◽  
Point To Point

A method for accurate registration on point clouds is presented in the paper. Manual alignment or the use of landmarks is avoided in the process of multi-view point clouds. Firstly, the differential geometric information is extracted from the point clouds. The extended Gaussian sphere and combination features are used to define the corresponding points of crude alignment. Secondly, the optimal algorithm，the point-to-point Iterated Closest Point, is applied to the accurate registration on point clouds. Thus, the complete point cloud can be obtained in the method.

scholarly journals The value distribution of harmonic mappings between Riemannian n-spaces

1975 ◽  
Vol 59 ◽  
pp. 45-58
Author(s):  
Hideo Imai
Keyword(s):  
Riemann Surface ◽  
Kernel Function ◽  
Riemann Surfaces ◽  
Distribution Theory ◽  
Value Distribution ◽  
Harmonic Mappings ◽  
Value Distribution Theory ◽  
Theoretic Method ◽  
Analytic Mapping ◽  
Crucial Part

We are concerned with the value distribution of a mapping of an open Riemannian n-space (n ≧ 3) into a Riemannian n-space. The value distribution theory of an analytic mapping of Riemann surfaces was initiated by S. S. Chern [1] and developed mainly by L. Sario [8], [9], [10], [11], and then by H. Wu [14], [15]. The most crucial part in Sario’s theory is the introduction of a kernel function on an arbitrary Riemann surface to describe appropriately the proximity of two points. His method indicates that the potential theoretic method is one of the powerful methods in the value distribution theory.

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