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Variational problems and PDEs in affine differential geometry

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Li H.

Banach Center Publications

2005

tom 69

nr 1

9-41

This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order PDEs. We consider classes of solutions satisfying these equations together with completeness conditions. We also formulate Bernstein problems and give partial solutions.

Ograniczanie wyników

1 Banach Center Publications

1 Li H.

1 2005

Wyniki wyszukiwania

Variational problems and PDEs in affine differential geometry