Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 171-179 (2002)

A Remark on Mixed Curvature Measures for Sets with Positive Reach

J. Rataj and M. Zähle

Charles University, Prague, Czech Republic; Friedrich-Schiller-University, Jena, Germany

Abstract: The existence of mixed curvature measures of two sets in ${\Bbb R}^d$ with positive reach introduced in [RZ] is discussed. An example shows that the non-osculating condition from [RZ] does not ensure the locally bounded variation of the mixed curvature measures. Further, some sufficient conditions for the local boundedness of mixed curvature measures involving absolute curvature measures are presented.

[RZ] Rataj, J.; Zähle, M.: Mixed curvature measures for sets of positive reach and a translative integral formula. Geom. Dedicata 57 (1995), 259-283.

Keywords: existence of mixed curvature measures; sets with positive reach; locally bounded variation; local boundedness; absolute curvature measures

Classification (MSC2000): 53C65

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