Variational problems and PDEs in affine differential geometry

• Autorzy: H. Z. Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53A15: Affine differential geometry
• 49Q05: Minimal surfaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 69
• Numer: 1
• Strony: 9-41

Daty

wydano

2005

Twórcy

autor

H. Z. Li

• Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China

Identyfikatory

DOI

10.4064/bc69-0-1