Geometric Inequalities Theory and Application of Convex Polytope in Space with Constant Curvature 

Author  PanJuanJuan 
Tutor  YangShiGuo 
School  Anhui University 
Course  Basic mathematics 
Keywords  Euclidean space Spherical space Hyperbolic space External dihedral angle Edge length Circumradii High Line Internal simplex Geometric inequalities 
CLC  O178 
Type  Master's thesis 
Year  2011 
Downloads  9 
Quotes  0 
This thesis to the geometry of high dimensional simplex inequality as the main research content . Use of distance geometry and convex geometry theory and algebraic methods and geometric inequality theory , Euclidean space , spherical space and hyperbolic space monomorphic geometric inequalities between the geometric quantities . text is divided into five chapters , the main content is as follows : in the first chapter introduces the history of the development of the convex body geometry , and mathematical workers at home and abroad in the convex body geometry , especially high dimensional simplex inequality achieved in the field of advanced research , and this made ??the second chapter first introduces related concepts simplex inscribed simplex , then established involving single circumradii , high Line and monomorphic class of Geometric Inequalities the inscribed monomorphic circumradii between , as a special case to promote the famous the n dimensional Eluer inequality . third chapter first introduces the concept of dihedral angle monomorphic , yet to see a single shaped outer the concept of dihedral angle bisector surface , this chapter gives the single concept shaped outer dihedral angle bisector surface , and then establish the the dihedral angle bisector area in the n  dimensional simplex formula given external dihedral angle the bisector surface area square and a lower bound estimate . fourth chapter first introduces several forms in Euclidean space Pedoe inequality , Some Inequalities involving Two volume , and to disseminate the ndimensional simplex the kn  type Pedoe inequality with kn type Pang  Chang inequality , and then study the ndimensional spherical space simplex geometric inequality problem , the establishment of the ndimensional spherical space for two n dimensional simplex edge length Pedoe inequality and Pang  Chang inequality , and obtain the spherical space is n dimensional simplex some new geometric inequalities fifth chapter first introduces the concept of hyperbolic space , then take advantage of the theories and methods of distance geometry , hyperbolic space Hn (k) , ndimensional high dimensional geometric simplex inequality problem involving the monomorphic volume of the ndimensional hyperbolic space , side area with edge length between certain geometric inequalities .