Affine Bernstein problems and Monge-Ampère equations
Affine differential geometry Monge-Ampère equations Mathematics sähkökirjat
World Scientific
2010
EISBN 9789812814173
Basic tools.
Local equiaffine hypersurfaces.
Local relative hypersurfaces.
The theorem of Jörgens-Calabi-Pogorelov.
Affine maximal hypersurfaces.
Hypersurfaces with constant affine mean curvature.
In 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 con
Local equiaffine hypersurfaces.
Local relative hypersurfaces.
The theorem of Jörgens-Calabi-Pogorelov.
Affine maximal hypersurfaces.
Hypersurfaces with constant affine mean curvature.
In 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 con
