On the smoothness of Hölder doubling measures

Author： Preiss D.  

Publisher： Springer Publishing Company

ISSN： 0944-2669

Source： Calculus of Variations and Partial Differential Equations, Vol.35, Iss.3, 2009-07, pp. : 339-363

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Abstract

It is known that in low dimensions supports of Hölder doubling measures are C1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale.

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