Uniformly Distributed Measures in Euclidean Spaces

F Ur Mathematik in Den Naturwissenschaften Leipzig Uniformly Distributed Measures in Euclidean Spaces

Local uniform rectifiability of uniformly distributed measures

The study of uniformly distributed measures was crucial in Preiss’ proof of his theorem on rectifiability of measures with positive density. It is known that the support of a uniformly distributed measure is an analytic variety. In this paper, we provide quantitative information on the rectifiability of this variety. Tolsa had already shown that n-uniform measures are uniformly rectifiable. Her...

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Uniformly distributed orbits of certain flows on homogeneous spaces

Let G be a connected Lie group, F be a lattice in G and U = {ut},~R be a unipotent one-parameter subgroup of G, viz. Adu is a unipotent linear transformation for all u ~ U. Consider the flow induced by the action of U (on the left) on G/F. Such a flow is referred as a unipotent flow on the homogeneous space G/F. The study of orbits of unipotent flows has been the subject of several papers. For ...

Network Location Problem with Stochastic and Uniformly Distributed Demands

This paper investigates the network location problem for single-server facilities that are subject to congestion. In each network edge, customers are uniformly distributed along the edge and their requests for service are assumed to be generated according to a Poisson process. A number of facilities are to be selected from a number of candidate sites and a single server is located at each facil...