Mixed Volumes and Volume Comparison Theorem = 혼합부피와부피비교이론

다국어 초록 (Multilingual Abstract)

In this notes, we obtain some geometric inequalities for mixed volumes of a convex bodv and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual. Also geometric inequalities for a simple closed plane curve in a Minkowski plane are obtained. A inequalities include Minkowskian perimeter of the curve and Euclidean area and Euclidean perimeter of isoperimetrix of the Minkowski plane. As an application of the inequality we develop the other geometric inequality involving area of centrally symmetric convex domain and its polar dual with respect to center.

목차 (Table of Contents)

• ABSTRACT
• 1.INTRODUCTION
• 2.PRELIMINARIES
• 3.MIXED VOLUMES AND COOMPPARISON THOREMS
• 4.GEOMETRIIC INEQUALITIES
• 5.INTEGRAALL FOMULAS AND GEOMETRIIC INEQUALITY
• REFERENCE