切线锥、维度和医学轴的前沿
The tangent cone, the dimension and the frontier of a medial axis
AI总结：
本文研究了医学轴在给定点处的切线锥与医学轴的维度关系，推导出医学轴维度的下界，并探讨了医学轴前沿可能产生问题的点的特征。
摘要：
本文旨在建立医学轴在给定点处的切线锥与医学轴的维度之间的关系。作为结果，得到了医学轴维度的下界，该下界以医学轴在该点处的维度表示。这似乎是描述医学轴维度完整描述的关键缺失环节。此外，还对医学轴前沿可能产生问题的点进行了进一步研究，结果以到达半径来刻画这些点的特征。
英文摘要：
This paper aims to establish a relation between the tangent cone of the medial axis of X at a given point a of R^n$ and the medial axis of the set of points in X realising the distance d(a,X). As a consequence, a lower bound for the dimension of the medial axis of X in terms of the dimension of the medial axis of m(a) is obtained. This appears to be the missing link to the full description of the medial axis' dimension. Further study of potentially troublesome points on the frontier of the medial axis is also provided, resulting in their characterisation in terms of the reaching radius.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
