ISSN:
1432-1297
Keywords:
Mathematics Subject Classification (1991): 53A15, 53A10, 53C45, 35J60
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. 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, R 2, must be a paraboloid. More generally, we shall consider the n-dimensional case, R n , 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 produce a counterexample showing that the Bernstein result does not hold in this generality for dimension n≥10.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002220000059
