scholarly journals Extreme problem for partially nonoverlapping domains on a Riemann sphere

2018 ◽  
Vol 235 (1) ◽  
pp. 74-80 ◽  
Author(s):  
Andrei L. Targonskii ◽  
Irina I. Targonskaya
Keyword(s):  
Riemann Sphere ◽  
Nonoverlapping Domains ◽  
Extreme Problem

Extreme problem for a mosaic system of points

2020 ◽  
Vol 17 (3) ◽  
pp. 437-447
Author(s):  
Andrii Targonskii ◽  
Iryna Targonskaya
Keyword(s):  
Complex Variable ◽  
Geometric Theory ◽  
Nonoverlapping Domains ◽  
Extreme Problem

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work.

Extreme problem for a mosaic system of points

2021 ◽  
Vol 252 (4) ◽  
pp. 558-565
Author(s):  
Andrii Leonidovych Targonskii ◽  
Iryna Igorivna Targonskaya
Keyword(s):  
Extreme Problem

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

Circular Arcs Fitted on a Riemann Sphere

1997 ◽  
Vol 67 (3) ◽  
pp. 311-317 ◽  
Author(s):  
Bjørn Lillekjendlie
Keyword(s):  
Riemann Sphere ◽  
Circular Arcs
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