Minimal Surfaces through Nevanlinna Theory

The study of minimal surfaces is an important subject in differential geometry, and Nevanlinna theory is an important subject in complex analysis and complex geometry. This book discusses the interaction between these two subjects. In particular, it describes the study of the value distribution properties of the Gauss map of minimal surfaces through Nevanlinna theory, a project initiated by the prominent differential geometers Shiing-Shen Chern and Robert Osserman.

• Presents the basis theory of minimal surfaces.
• Develops the classical theory of holomorphic curves in the projective space with Ahlfors' approach

• Examines the y the value distribution properties for the Gauss maps of the immersed harmonic surfaces.