Liping Yuan

activity

20122026

collaborators

9 papers

math.CO2026

On the m-point convexity

Wenzhi Liu, Wei Wang, Liping Yuan +1

Let $S \subset R^{d}$ $(d \geq 2)$ . A set $S$ is said to be $m$ -point convex, if for every $m$ distinct points in $S$ , at least one of the line-segments determined by them lie…

math.CO2026

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…

math.CO2025

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…

math.FA2025

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…

math.CO2025

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.

math.MG2019

Locating diametral points

Jin-ichi Itoh, Costin Vîlcu, Liping Yuan +1

Let $K$ be a convex body in $R^{d}$ , with $d = 2, 3$ . We determine sharp sufficient conditions for a set $E$ composed of $1$ , $2$ , or $3$ points of $bd K$ , to contain a…

math.CO2017

A note on discrete lattice-periodic sets with an application to Archimedean tilings

Matthias Schymura, Liping Yuan

Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of…

math.CO2014

Volumes of convex lattice polytopes and a question of V. I. Arnold

Imre Barany, Liping Yuan

We show by a direct construction that there are at least $exp {c V^{(d - 1) / (d + 1)}}$ convex lattice polytopes in $R^{d}$ of volume $V$ that are different in the sense that no…

math.CO2012

Acute Triangulations of the Cuboctahedral Surface

Xiao Feng, Liping Yuan

In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the b…