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Aljosa Volcic

Publications and source records attributed to Aljosa Volcic.

5 recordsLinked to original sources
arXiv2012

Convergence in shape of Steiner symmetrizations

There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examples show that Steiner symmetrization along a sequence of directions whose differences are square summable does not generally converge. (Note that this may happen even with sequences of directions which are dense in S^{n-1}.) Here we show that such sequences converge in shape. The limit need not be an ellipsoid or even a convex set. We also deal with uniformly distributed sequences of directions, and with a recent result of Klain on Steiner symmetrization along sequences chosen from a finite set of directions.

math.MG↗
arXiv2010

Uniform distribution on the sphere and caps

In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphere.

math.CA↗
arXiv2009

Random symmetrizations of measurable sets

In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets, paralleling a result due to Mani-Levitska concerning convex bodies.

math.PR↗
arXiv2009

A generalization of Kakutani's splitting procedure

In this paper we will study uniformly distributed sequences of partitions of [0,1], a concept which has been introduced by Kakutani in 1976. We will construct new families of u.d. sequences of partitions and study relations with the classical concept of uniformly distributed sequences of points.

math.NT↗