Hausdorff Dimension of the Nondifferentiability Set of a Convex Function

Abstract

We find an upper bound for the Hausdorff dimension of the nondifferentiability set of a countinuous convex function defined on a Riemannian manifold, and as an application we show that the Hausdorff dimention of nondifferentiability points of a hypersurface in $R^{n}$ which is boundary of an open convex subset, is at most n-2.