Title Page
Contents
ABSTRACT 6
1. Introduction 7
2. Proof by using the Knothe map 10
2.1. Construction of the Knothe map 11
2.2. Computation of determinant ∇M 13
2.3. Proof of the isoperimetric inequality 15
2.4. The simple case 17
3. Proof by using ABP method 20
3.1. Proof of the isoperimetric inequality 20
3.2. Proof of the weighted isoperimetric inequality in convex cones 24
4. Isoperimetric regions in Gaussian space 32
References 35
ABSTRACT IN KOREAN 38