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5 papers
On Lambda Function and a Quantification of Torhorst Theorem
Li Feng, Jun Luo, Xiao-Ting Yao
To any compact we associate a map -- the lambda function of -- such that a planar continuu…
Ricci-flat graphs with girth four
Weihua He, Jun Luo, Chao Yang +1
Lin-Lu-Yau introduced an interesting notion of Ricci curvature for graphs and obtained a complete characterization for all Ricci-flat graphs with girth at least five [1]. In this p…
Peano Model for Planar Compacta and a Lemma by Beardon
Jun Luo, Yi Yang, Xiao-Ting Yao
It is known that, among all the monotone decompositions of a planar compact set K with Peano hyperspaces, there exists a unique one that is finer than all the others. We call it th…
Every component of a fractal square is a Peano continuum
Jun Luo, Hui Rao, Ying Xiong
This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or…
Fibers and local connectedness of planar continua
Benoît Loridant, Jun Luo
We describe non-locally connected planar continua via the concepts of fiber and numerical scale. Given a continuum and , we show that the set o…