Displaying similar documents to “Compact convex bodies with one curvature measure near the surface measure.”

On set covariance and three-point test sets

Jan Rataj (2004)

Czechoslovak Mathematical Journal

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The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of ℝ d is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives...

The mean curvature measure

Quiyi Dai, Neil S. Trudinger, Xu-Jia Wang (2012)

Journal of the European Mathematical Society

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We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions...

The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

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The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.