scholarly journals Drawing Cone Spherical Metrics via Strebel Differentials

2018 ◽  
Vol 2020 (11) ◽  
pp. 3341-3363 ◽  
Author(s):  
Jijian Song ◽  
Yiran Cheng ◽  
Bo Li ◽  
Bin Xu
Keyword(s):  
Constant Curvature ◽  
Riemann Surfaces ◽  
Conformal Metrics ◽  
Conical Singularities ◽  
Ribbon Graphs ◽  
New Class ◽  
Compact Riemann Surfaces

Abstract Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. By using Strebel differentials as a bridge, we construct a new class of cone spherical metrics on compact Riemann surfaces by drawing on the surfaces some class of connected metric ribbon graphs.

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

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.

scholarly journals Isospectral flat connexions

2013 ◽  
Vol 31 (2) ◽  
pp. 279
Author(s):  
S. Srinivas Rau ◽  
Sudhamsh Reddy
Keyword(s):  
Riemann Surfaces ◽  
Higher Rank ◽  
Compact Riemann Surfaces

Isospectral flat connexions are constructed for higher rank bundlesover compact Riemann surfaces

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