Remarks on a translative formula for sets of positive reach

被引：4

作者：

Rataj, J ^{[1
]}

机构：

[1] CHARLES UNIV,MATEMAT USTAV,PRAGUE 18600 8,CZECH REPUBLIC

来源：

GEOMETRIAE DEDICATA | 1997年 / 65卷 / 01期

关键词：

principal kinematic formula; translative integral geometry; set of positive reach; differentiable extension; fractal set;

D O I：

10.1023/A:1004912401199

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An example of a pair of sets of positive reach is presented, violating a condition assuring the intersection of these sets to have positive reach for almost all translations of one of these sets. The same condition ensures the validity of a translative formula proved recently in Geom. Dedicata 57 (1995), 259-283.

引用

页码：59 / 62

页数：4

共 5 条

[1] FEDER H, 1969, GEOMETRIC MEASURE TH
[2] Federer H., 1959, Trans. Amer. Math. Soc., V93, P418, DOI [DOI 10.1090/S0002-9947-1959-0110078-1, 10.1090/S0002-9947-1959-0110078-1, DOI 10.2307/1993504]
[3] MIXED CURVATURE MEASURES FOR SETS OF POSITIVE REACH AND A TRANSLATIVE INTEGRAL FORMULA
RATAJ, J
ZAHLE, M
[J]. GEOMETRIAE DEDICATA, 1995, 57 (03) : 259 - 283
[4] TRANSLATIVE AND KINEMATIC INTEGRAL FORMULAS FOR CURVATURE MEASURES
SCHNEIDER, R
WEIL, W
[J]. MATHEMATISCHE NACHRICHTEN, 1986, 129 : 67 - 80
[5] INTEGRAL AND CURRENT REPRESENTATION OF FEDER CURVATURE MEASURES
ZAHLE, M
[J]. ARCHIV DER MATHEMATIK, 1986, 46 (06) : 557 - 567

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