In this thesis, we shall survey the construction of minimal surface in closed three-manifold via min-max construction.
Our focus will be on the existence of the min-max stationary varifold via this construction. There are many different type min-max construction. Our main reference is The min-max construction of minimal surfaces [CD] by Colding and De Lellis in which they apply min-max method in the isotopy class of generalized family of surfaces. We shall also mention some other min-max method in the introduction part.
