Spherical type surfaces via support function

Abstract: In this work we define the surfaces spherical type via support function (in short, SS-surfaces). We present a Weierstrass type representation for SS-surfaces with prescribed Gauss map which depends on two holomorphic functions. Also, we use this representation to classify the surfaces of rotation. Moreover, we show that every compact and connected SS-surface is the sphere and we give explicit examples of SS-surfaces.