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Hyperbolic Geometric Flow-Review and Ideas

Author: ZhouYanYan
Tutor: LiuKeFeng
School: Zhejiang University
Course: Basic mathematics
Keywords: Hyperbolic geometry flow Dissipative hyperbolic geometry stream Einstein metrics Exact solution Volatility Short existence and uniqueness Nonlinear Stability Hyperbolic mean curvature flow Riemann surface
CLC: O186.12
Type: Master's thesis
Year: 2010
Downloads: 60
Quote: 0
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Abstract


This article is a review article , a brief introduction by the Kong Dexing , and Liu Kefeng introduced and studied hyperbolic geometry streams Finally, some of the ideas flow of hyperbolic geometry . Consists of the following main chapters. The first chapter focuses on the flow of hyperbolic geometry concepts and some basic properties , we have a preliminary understanding of the flow of hyperbolic geometry is the study of differential geometry and relativity of some important issues is a powerful tool . The second chapter introduces the dissipative term with some properties of hyperbolic geometry and hyperbolic flow Ricci soliton theory of dissipative hyperbolic geometry derived curvature flow volatility of short-term existence and uniqueness of solutions of the nonlinear stability Riemann surface resistance and dissipation of the whole classical hyperbolic geometry stream existence and Nonexistence other theories . The third chapter discusses the hyperbolic geometry exact solution flow through the exact solutions of these morphological analysis drawn relevant conclusions , which helps us to stream on the basic features of hyperbolic geometry understanding also helps us in general Einstein equation understanding. Chapter IV introduces hyperbolic mean curvature flow some basic properties , and then study hyperbolic mean curvature flow : the evolution of a plane curve , the curve of the support function , derived a hyperbolic Monge-Ampere equation . On this basis , we prove the existence and uniqueness of the local . For future research , also studied the dissipative hyperbolic mean curvature flow . Finally, we introduced the hyperbolic mean curvature flow plane curve singularity formation movement , has been the breakdown of the results for solutions and gives an accurate understanding of the life span of estimates. Chapter V gives the hyperbolic geometry stream some open issues.

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Differential geometry,integral geometry > Differential Geometry > Riemannian geometry
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