Asymptotics of CMC surfaces with polynomial Hopf differential

2004 ◽  
Vol 19 (3) ◽  
pp. 257-267
Author(s):  
G. Dos Reis
Keyword(s):  
Cmc Surfaces ◽  
Hopf Differential

scholarly journals DPW potentials for compact symmetric CMC surfaces in S3

2020 ◽  
Vol 156 ◽  
pp. 103791
Author(s):  
Benedetto Manca
Keyword(s):  
Cmc Surfaces

scholarly journals The Harmonic Mapping Whose Hopf Differential Is a Constant

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1310
Author(s):  
Liang Shen
Keyword(s):  
Unit Disk ◽  
Harmonic Mapping ◽  
Hyperbolic Metric ◽  
Beltrami Coefficient ◽  
Hopf Differential ◽  
The Hyperbolic Metric

Suppose that h(z) is a harmonic mapping from the unit disk D to itself with respect to the hyperbolic metric. If the Hopf differential of h(z) is a constant c>0, the Beltrami coefficient μ(z) of h(z) is radially symmetric and takes the maximum at z=0. Furthermore, the mapping γ:c→μ(0) is increasing and gives a homeomorphism from (0,+∞) to (0,1).

scholarly journals Harmonic maps and wild Teichmüller spaces

2019 ◽  
pp. 1-45
Author(s):  
Subhojoy Gupta
Keyword(s):  
Riemann Surface ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Hyperbolic Surface ◽  
Teichmuller Space ◽  
Quadratic Differentials ◽  
Hopf Differential ◽  
Principal Parts

We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has noncompact ends with boundary cusps. This extends Wolf’s parametrization of the Teichmüller space of a closed surface using holomorphic quadratic differentials. Our proof involves showing the existence of a harmonic map from a punctured Riemann surface to a crowned hyperbolic surface, with prescribed principal parts of its Hopf differential which determine the geometry of the map near the punctures.

scholarly journals A spectral curve approach to Lawson symmetric CMC surfaces of genus 2

2014 ◽  
Vol 360 (3-4) ◽  
pp. 607-652 ◽  
Author(s):  
Sebastian Heller
Keyword(s):  
Spectral Curve ◽  
Cmc Surfaces ◽  
Genus 2

scholarly journals On Hawking mass and Bartnik mass of CMC surfaces

2020 ◽  
Vol 27 (3) ◽  
pp. 855-885
Author(s):  
Pengzi Miao ◽  
Yaohua Wang ◽  
Naqing Xie
Keyword(s):  
Cmc Surfaces
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