ON THE CHARACTERIZATION OF SOME CLASSES OF PROXIMALLY SMOOTH SETS

被引：11
作者：
Crasta, Graziano [1 ]
Fragala, Ilaria [2 ]
机构：
[1] Univ Roma 1, Dipartimento Matemat G Castelnuovo, Ple A Moro 2, I-00185 Rome, Italy
[2] Politecn Milan, Dipartimento Matemat, Piazza Leonardo Vinci 32, I-20133 Milan, Italy
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2016年 / 22卷 / 03期
关键词：
Distance function; proximal smoothness; positive reach; cut locus; central set; skeleton; medial axis; DISTANCE FUNCTION; TORSIONAL RIGIDITY; CURVATURE MEASURES; MEDIAL AXIS; REGULARITY; SINGULARITIES; CONVEXITY; BOUNDARY; DOMAINS;
D O I：
10.1051/cocv/2015022
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We provide a complete characterization of closed sets with empty interior and positive reach in R-2. As a consequence, we characterize open bounded domains in R-2 whose high ridge and cut locus agree, and hence C-1 planar domains whose normal distance to the cut locus is constant along the boundary. The latter result extends to convex domains in R-n.
引用
收藏
页码：710 / 727
页数：18
相关论文
共 48 条
[1]   Singular gradient flow of the distance function and homotopy equivalence [J].
Albano, P. ;
Cannarsa, P. ;
Nguyen, Khai T. ;
Sinestrari, C. .
MATHEMATISCHE ANNALEN, 2013, 356 (01) :23-43
[2]   ON THE STRUCTURE OF SINGULAR SETS OF CONVEX-FUNCTIONS [J].
ALBERTI, G .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (01) :17-27
[3]  
Alexandrov A. D., 1962, AM SOC T, V31, P341
[4]  
Ambrosio L, 2000, CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, P5
[5]  
[Anonymous], 2010, Handbook of nonconvex analysis
[6]  
[Anonymous], 1994, Metodi diretti nel Calcolo delle Variazioni
[7]   SETS WITH POSITIVE REACH [J].
BANGERT, V .
ARCHIV DER MATHEMATIK, 1982, 38 (01) :54-57
[8]  
Bellettini G, 2007, J CONVEX ANAL, V14, P353
[9]  
Bernard F, 2006, J CONVEX ANAL, V13, P525
[10]   A central set of dimension 2 [J].
Bishop, Christopher J. ;
Hakobyan, Hrant .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (07) :2453-2461
12345