On set covariance and three-point test sets

Jan Rataj

Displaying similar documents to “On set covariance and three-point test sets”

Comparison between the generalized mean curvature according to Allard and Federer's mean curvature measure

E. Ossanna (1992)

Rendiconti del Seminario Matematico della Università di Padova

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An upper estimation for the eigenfrequencies of vibrating Liapunoff bodies (first boundary value problem).

Joo, I., Stacho, L.L. (1981)

Publications de l'Institut Mathématique. Nouvelle Série

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Compact convex bodies with one curvature measure near the surface measure.

Peter Kohlmann (1995)

Journal für die reine und angewandte Mathematik

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Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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In some recent work, fractal curvatures $C_{k}^{f} (F)$ and fractal curvature measures $C_{k}^{f} (F, \cdot)$ , $k = 0, ..., d$ , have been determined for all self-similar sets $F$ in $ℝ^{d}$ , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...

$K$ -distance sets, Falconer conjecture, and discrete analogs.

Iosevich, A., Łaba, I. (2005)

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Mean curvature of a measure and related variational problems

Guy Bouchitté, Giuseppe Buttazzo, Ilaria Fragalà (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Non-parametric convex hypersurfaces with a curvature restriction

Rolf Schneider (1983)

Annales Polonici Mathematici

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On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane

Tomáš Mrkvička, Jan Rataj (2009)

Kybernetika

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A method of estimation of intrinsic volume densities for stationary random closed sets in $ℝ^{d}$ based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation...