Limit sections and universal points of convex surfaces

Surfaces with Central Convex Cross-sections

Say that a surface in S ⊂ R has the central plane oval property, or cpo, if • S meets some affine plane transversally along an oval, and • Every such transverse plane oval on S has central symmetry. We show that a complete, connected C surface with cpo must either be a cylinder over a central oval, or else quadric. We apply this to deduce that a complete C surface containing a transverse plane ...

Universal points of convex bodies and bisectors in Minkowski spaces

We deal with different properties of a smooth and strictly convex body that depend on the behavior of the planar sections of the body parallel to and close to a given tangent plane. The first topic is boundary points where any given convex domain in the tangent plane can be approximated by a sequence of suitably rescaled planar sections (so-called p-universal points). In the second topic, the g...

Euclidean sections of convex bodies

This is a somewhat expanded form of a four hours course given, with small variations, first at the educational workshop Probabilistic methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks later at the Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity, Kent, Ohio, August 13-20, 2008. The main part of these notes gives yet a...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

On Lacunary Statistical Limit and Cluster Points of Sequences of Fuzzy Numbers

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [...