Trudinger, Neil; Wang, Xu-Jia
In this paper, we prove the validity of the Chern conjecture in affine geometry , 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]
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