On Spacelike Complete Stationary Genus 0 Surfaces With Regular Flat Embedded Ends In R₁⁴

The purpose of this master thesis is mainly to consider the complete spacelike stationary surfaces with regular flat embedded ends and its related problems in R₁⁴,which is based on the related theory of minimal surfaces in R³.The main content of the thesis is divided into five chapters.In Chapter one,we introduce the research background and briefly describe the main results obtained in this paper.In Chapter two,we introduce the geometry of the spacelike stationary surfaces in R₁⁴.It mainly includes the Weierstrass representation of the spacelike stationary sur-faces in R₁⁴,the concept of end and the Lorentz deformation of the spacelike stationary surfaces in R₁⁴.In Chapter three,we focus on the complete spacelike stationary genus 0 surfaces with regular flat embedded ends in R₁⁴.We will use the Lorentz deformation of space-like stationary surfaces in R₁⁴to give the concrete construction of examples of the complete spacelike stationary genus 0 surfaces with regular flat embedded ends,and the proof of non-existence theorem.In Chapter four,we compute examples of genus 0 complete minimal surfaces with flat embedded ends in R³and discuss the properties of the ends of these examples,which come from Peng C.K.and Xiao L.in[39].At the same time,the non-existence theorem is given for the minimal surface with 4 vertical flat embedded ends in R³.In Chapter five,we briefly summarize the research content of this thesis and propose the problems of the next step.