Hausdorff Dimension of the Nondifferentiability Set of a Convex Function

Reza Mirzaie


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.

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