Quasi-rectifying Curves And The Classification Of Limit Sets

The main purpose of this thesis is to investigate the quasi-rectifying curves inMinkowski space, classify the limit points of complex hyperbolic isometry groupsand compare with the case in real hyperbolic spaceand and discuss the monotonic-ity and logarithmic convexity of a function involving the gamma function.The paper has three parts.Chapter 1 introduces the background information of curves in Minkowskispace, and some basic concepts of Minkowski space, defines the quasi-rectifyingcurves in Minkowski space, and proves some properties of quasi-rectifying curves.Chapter 2 introduces the background of complex hyperbolic geometry, somebasic concepts of complex hyperbolic space, complex hyperbolic isometry groupsand Dirichlet polyhedra, review the results of the limit sets of discrete M¨obiusgroups, finally, gives the classification of limit points and emphasizes to comparewith two limit points.Chapter 3 introduces the background of gamma function, and some basicconcepts of gamma function and its logarithmic derivative function, gives andproves some lemmas and theorems.