On one-dimensional continua uniformly approximating planar sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On one-dimensional continua uniformly approximating planar sets

Authors:

Michele Miranda Jr Emanuele Paolini Eugene Stepanov

Institution:

(1) Dipartimento di Matematica “E. De Giorgi”, Università di Lecce, C.P. 193, 73100 Lecce, Italy;(2) Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy;(3) Dipartimento di Matematica “L. Tonelli”, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy

Abstract:

Consider the class of closed connected sets $\Sigma\subset {\cal R}^n$ satisfying length constraint ${\cal H}(\Sigma)\leq l$ with given l>0. The paper is concerned with the properties of minimizers of the uniform distance F _M of Σ to a given compact set $M\subset {\cal R}^n$ ,

$F_M(\Sigma):= \max_{y\in M} dist(y,\Sigma),$

(22)

where dist(y, Σ) stands for the distance between y and Σ. The paper deals with the planar case n=2. In this case it is proven that the minimizers (apart trivial cases) cannot contain closed loops. Further, some mild regularity properties as well as structure of minimizers is studied.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏