5 papers
On the m-point convexity
Wenzhi Liu, Wei Wang, Liping Yuan +1
Let . A set is said to be -point convex, if for every distinct points in , at least one of the line-segments determined by them lie…
The orthogonal connectedness of polyhedral surfaces
Julia Q. Du, Xuemei He, Xiaotian Song +3
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doi…
Excursions in Sylvester-Gallai land
Imre Barany, Julia Q. Du, Dan Schwarz +2
The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessa…
On Klee's problem of convex bodies in Banach spaces
Lixin Cheng, Chunlan Jiang, Liping Yuan
It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infi…
Orthogonally connected sets
Xuemei He, Xiaotian Song, Liping Yuan +1
In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.