Global Affine Differential Geometry of Hypersurfaces

"From Review for the first edition by R.Walter (Dortmund) in Zenralblatt MATH: ""This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. [...] Moreover, the recent development revealed that affine differential geometry - as differential geometry in general - has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces (in the complex- analytic sense). The core of the text is devoted to four important subfields [...]: Affine hyperspheres; Rigidity and uniqueness theorems; Variational problems and affine maximal surfaces; Geometric inequalities. There is a comprehensive introduction [...], starting at the level of students with a general background in Euclidean differential geometry and basic Riemannian geometry. [...] The bibliography contains about 625 items [...], such that researchers and newcomers are provided with an almost complete list, starting right with the beginnings. The book is written in a clear style, and almost all proofs are carried out in detail. Even auxiliary parts from other fields are explained and sometimes proved. This underlines in addition, how close this field is to the broad flow of modern mathematics. [...] Summary: This is a fine book, inviting to an active and interesting field of research."""