Harmonic mappings and conformal minimal immersions of Riemann surfaces into $${\mathbb {R}^{\rm N}}$$

2012 ◽  
Vol 47 (1-2) ◽  
pp. 227-242 ◽  
Author(s):  
Antonio Alarcón ◽  
Isabel Fernández ◽  
Francisco J. López
Keyword(s):  
Riemann Surfaces ◽  
Harmonic Mappings ◽  
Minimal Immersions

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.

scholarly journals Harmonic mappings and moduli spaces of Riemann surfaces

2009 ◽  
Vol 14 (1) ◽  
pp. 171-196 ◽  
Author(s):  
Jürgen Jost ◽  
Shing Tung Yau
Keyword(s):  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Harmonic Mappings
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