Surface volume and minimal surfaces

This thesis consists of four chapters. The first chapter is the introduction part of this thesis.In the second chapter, the basic concepts and theorems used in the other chapters are given.In the third chapter, the volumes of n-surfaces in Rn+1 are given in terms of the coordinate vector fields. In the special case n = 1 and n = 2 it is seen that the volume formula gives the length of a curve and the area of a surface, respectively. Moreover the volume of n-dimensional surface in Rn+k is obtained by the help of volume form C,.In the last chapter, it is mentioned about the minimal surfaces. Some properties about minimal surface volume are given.KEY WORDS: Surface, orientation, area, volume, volume form, minimal surface