arXiv subjects

Maxim Tkachuk

Publications and source records attributed to Maxim Tkachuk.

2 recordsLinked to original sources

arXiv2015

On the shadow problem and its generalizations to ellipsoids

The main goal of the paper is to solve some problems about shadow for the sphere generalized on the case of the ellipsoid. Here, the essence of the problem is to find the the minimal number of non-overlapping balls with centers on the sphere which are not holding the center of the sphere and such that every line passing through the center of the sphere would intersect at least one of the balls. Another method of solving the shadow problem for the sphere is also proposed.

math.MG↗

arXiv2013

Theorems about includings for multivalued mappings

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a coacute angle condition" or "a strict coacute angle condition". There also were obtained similar results for restrictions of multivalued mappings satisfying some metric limitations.

math.CV↗