02631nam 2200589 a 450 991045619840332120200520144314.01-282-76028-99786612760280981-281-417-5(CKB)2490000000001891(EBL)731103(OCoLC)670429445(SSID)ssj0000411378(PQKBManifestationID)12144841(PQKBTitleCode)TC0000411378(PQKBWorkID)10355870(PQKB)10248696(MiAaPQ)EBC731103(WSP)00006835(Au-PeEL)EBL731103(CaPaEBR)ebr10422548(CaONFJC)MIL276028(EXLCZ)99249000000000189120100803d2010 uy 0engur|n|---|||||txtccrAffine Bernstein problems and Monge-Ampère equations[electronic resource] /An-Min Li ... [et al.]Singapore ;Hackensack, N.J. World Scientificc20101 online resource (192 p.)Description based upon print version of record.981-281-416-7 Includes bibliographical references (p. 173-177) and index.Preface; Contents; 1. Basic Tools; 2. Local Equiaffine Hypersurfaces; 3. Local Relative Hypersurfaces; 4. The Theorem of Jorgens-Calabi-Pogorelov; 5. Affine Maximal Hypersurfaces; 6. Hypersurfaces with Constant Affine Mean Curvature; Bibliography; IndexIn this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It is well-known that many geometric problems in analytic formulation lead to important classes of PDEs. The focus of this monograph is on variational problems and higher order PDEs for affine hypersurfaces. Affine maximal hypersurfaces are extremals of the interior variation of the affinely invariant volume. The corresponding Euler-Lagrange equation is a highly complicated nonlinear fourth order PDE. In recent years, the global study of such fourth order PDEs has received conAffine differential geometryMonge-Ampère equationsElectronic books.Affine differential geometry.Monge-Ampère equations.516.36Li An-Min1946-924826MiAaPQMiAaPQMiAaPQBOOK9910456198403321Affine Bernstein problems and Monge-Ampère equations2075789UNINA