@Article{JMS-58-22,
author = {Su , XiaoleSun , Hongwei and Wang , Yusheng},
title = {Quasi-Convex Subsets and the Farthest Direction in Alexandrov Spaces with Lower Curvature Bound},
journal = {Journal of Mathematical Study},
year = {2025},
volume = {58},
number = {1},
pages = {22--37},
abstract = {<p style="text-align: justify;">Let $F$ be a closed subset in a finite dimensional Alexandrov space $X$ with
lower curvature bound. This paper shows that $F$ is quasi-convex if and only if, for any
two distinct points $p,r∈F,$ if there is a direction at $p$ which is more than $\frac{π}{2}$ away from $⇑^r_p$ (the set of all directions from $p$ to $r$), then the farthest direction to $⇑^r_p$ at $p$ is tangent
to $F.$ This implies that $F$ is quasi-convex if and only if the gradient curve starting from $r$ of the distance function to $p$ lies in $F.$ As an application, we obtain that the fixed
point set of an isometry on $X$ is quasi-convex.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v58n1.25.02},
url = {http://global-sci.org/intro/article_detail/jms/23936.html}
}