scholarly journals Representation of Maximal Surfaces in a 3-Dimensional Lightlike Cone

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1921
Author(s):  
Jinhua Qian ◽  
Xueshan Fu ◽  
Huili Liu
Keyword(s):  
Differential Equation ◽  
Function Theory ◽  
Complex Function ◽  
Representation Formula ◽  
Complex Function Theory ◽  
Maximal Surfaces ◽  
3 Dimensional ◽  
Differential Equation Theory

In this paper, the representation formula of maximal surfaces in a 3-dimensional lightlike cone Q3 is obtained by making use of the differential equation theory and complex function theory. Some particular maximal surfaces under a special induced metric are presented explicitly via the representation formula.

Function Theoretic Integral Operator Methods for Partial Differential Equations(1)

1980 ◽  
Vol 23 (2) ◽  
pp. 127-135
Author(s):  
Erwin Kreyszig
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Harmonic Functions ◽  
Complex Analysis ◽  
Function Theory ◽  
Complex Function ◽  
Complex Function Theory ◽  
Partial Differential ◽  
Linear Partial Differential Equations

It is well known that complex analytic functions and harmonic functions of two real variables are closely related, so that from methods and results in complex function theory one can easily obtain theorems on those harmonic functions. This is the prototype of a relation between complex analysis and a partial differential equation (Laplace's equation in two variables). In the case of more general linear partial differential equations, one can establish similar relations.

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