03658nam 2200697 450 991078882030332120230807210931.03-11-039090-63-11-026889-210.1515/9783110268898(CKB)3360000000514892(EBL)1663180(SSID)ssj0001530691(PQKBManifestationID)12559968(PQKBTitleCode)TC0001530691(PQKBWorkID)11529905(PQKB)10446789(MiAaPQ)EBC1663180(DE-B1597)173732(OCoLC)921228113(OCoLC)979970990(DE-B1597)9783110268898(Au-PeEL)EBL1663180(CaPaEBR)ebr11087965(CaONFJC)MIL821097(EXLCZ)99336000000051489220150820h20152015 uy 0engur|n|---|||||txtccrGlobal affine differential geometry of hypersurfaces /An-Min Li [and three others]Second revised and extended edition.Berlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2015.©20151 online resource (378 p.)De Gruyter Expositions in Mathematics,0938-6572 ;Volume 11Description based upon print version of record.3-11-026667-9 Includes bibliographical references and index.Frontmatter -- Contents -- Introduction -- 1. Preliminaries and basic structural aspects -- 2. Local equiaffine hypersurface theory -- 3. Affine hyperspheres -- 4. Rigidity and uniqueness theorems -- 5. Variational problems and affine maximal surfaces -- 6. Hypersurfaces with constant affine Gauß-Kronecker curvature -- 7. Geometric inequalities -- A. Basic concepts from differential geometry -- B. Laplacian comparison theorem -- Bibliography -- Index -- BackmatterThis 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.The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof. De Gruyter expositions in mathematics ;Volume 11.Global differential geometryHypersurfacesAffine differential geometry.Global differential geometry.Hypersurfaces.Global differential geometry.Hypersurfaces.516.3/62Li An-Min, 726115Li AnminMiAaPQMiAaPQMiAaPQBOOK9910788820303321Global affine differential geometry of hypersurfaces3764866UNINA