The Bernstein problem for affine maximal hypersurfaces
Description
In this paper, we prove the validity of the Chern conjecture in affine geometry [18], namely that an affine maximal graph of a smooth, locally uniformly convex function on two dimensional Euclidean space, R2, must be a paraboloid. More generally, we shall consider the n-dimensional case, Rn, showing that the corresponding result holds in higher dimensions provided that a uniform, "strict convexity" condition holds. We also extend the notion of "affine maximal" to non-smooth convex graphs and...[Show more]
Collections | ANU Research Publications |
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Date published: | 2000 |
Type: | Journal article |
URI: | http://hdl.handle.net/1885/90182 |
Source: | Inventiones Mathematicae |
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File | Description | Size | Format | Image |
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01_Trudinger_The_Bernstein_problem_for_2000.pdf | 161.5 kB | Adobe PDF | Request a copy |
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