46 citations · 149 across the 14 of their papers we have counts for
4 papers · 1 filter
Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces
Jan Rataj, Ludek Zajicek
Let be a closed set and or . S. Ferry (1975) proved that then, for almost all , the level set (distance sphere, -boundary) $S_r(F):= \{x \in \R^…
Approximations of the Wiener sausage and its curvature measures
Jan Rataj, Evgeny Spodarev, Daniel Meschenmoser
A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random pol…
On Volume and Surface Area of Parallel Sets
Jan Rataj, Steffen Winter
The r-parallel set to a set A in a Euclidean space consists of all points with distance at most r from A. We clarify the relation between the volume and the surface area of paralle…
Properties of distance functions on convex surfaces and applications
Jan Rataj, Ludek Zajicek
If is a convex surface in a Euclidean space, then the squared intrinsic distance function $\dist^2(x,y)$ is DC (d.c., delta-convex) on in the only natural extrinsic…