scholarly journals Normal family theory and Gauss curvature estimate of minimal surfaces in $\mathbb{R}^m$

2016 ◽  
Vol 103 (2) ◽  
pp. 297-318 ◽  
Author(s):  
Xiaojun Liu ◽  
Xuecheng Pang
Keyword(s):  
Minimal Surfaces ◽  
Normal Family ◽  
Gauss Curvature ◽  
Curvature Estimate ◽  
Family Theory

scholarly journals A uniqueness problem for entire functions related to Brück’s conjecture

2018 ◽  
Vol 68 (4) ◽  
pp. 823-836
Author(s):  
Nguyen Van Thin ◽  
Ha Tran Phuong ◽  
Leuanglith Vilaisavanh
Keyword(s):  
Entire Function ◽  
Uniqueness Theorem ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Entire Functions ◽  
Uniqueness Problem ◽  
Family Theory

Abstract In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Brück. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et al. [14]. However, our method differs the method of L. Z. Yang et al. [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].

scholarly journals Nambu-Goto Strings viaWeierstrass Representation

2017 ◽  
Vol 13 (4) ◽  
pp. 4985-4992
Author(s):  
Mahmoud Kotb
Keyword(s):  
Gauge Theory ◽  
Physical Properties ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
String Model ◽  
Gauss Curvature ◽  
Weierstrass Representation ◽  
Perturbative Solution ◽  
Goto Action

A description of string model of gauge theory are related to minimal surfaces. notations of minimal surface and related mean and Gauss curvature discussed. The Weierstrass representation for a surface conformally which immersed in R used to represent Nambu- Goto action, action of Nambu Goto is calculated usingWeierstrass representation which can be used to calculate the Partion Function and potential, then a non-perturbative solution for action is aimed and fulfilled and a consequences of that are investigated and its mathematical and physical properties are discussed.

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