The affine Plateau problem
classification
🧮 math.DG
math.AP
keywords
affineproblemhypersurfacesplateauanalogueappropriateareaboundary
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In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.
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