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  • Springer  (2)
  • 1975-1979  (2)
  • 1978  (2)
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  • Springer  (2)
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  • 1975-1979  (2)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Über Tangentialkörper der Kugel (1978)
    Springer
    Manuscripta mathematica 23 (1978), S. 269-278 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The convex body K is called a p-tangential body of the convex body $$\bar K$$ if $$\bar K \subseteq K$$ and every (n−p−1)-extremal support plane of K is also a support plane of ¯K. It has been conjectured by Minkowski and proved by Bol that 1-tangential bodies of balls are characterized by the case of equality in one of the Minkowski inequalities for the quermassintegrals. This fact, together with a geometric description of the support of the surface area function Sp(K,·) of order p which was obtained earlier by the author, is used to prove some new characterizations of p-tangential bodies. For instance, an n-dimensional convex body K is a p-tangential body of a ball (for some p∈{0,..., n−2}) if, and only if, its surface area functions Sp (K,·) and Sn−1 (K,·) are constant multiples of each other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171753
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  • 2
    Electronic Resource
    Electronic Resource
    Curvature measures of convex bodies (1978)
    Springer
    Annali di matematica pura ed applicata 116 (1978), S. 101-134 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The curvature measures, introduced by Federer for the sets of positive reach, are investigated in the special case of convex bodies. This restriction yields additional results. Among them are:(5.1), an integral-geometric interpretation of the curvature measure of order m, showing that it measures, in a certain sense, the affine subspaces of codimension m+1 which touch the convex body;(6.1), an axiomatic characterization of the (linear combinations of) curvature measures similar to Hadwiger's characterization of the quermassintegrals of convex bodies;(8.1), the determination of the support of the curvature measure of order m, which turns out to be the closure of the m-skeleton of the convex body. Moreover we give, for the case of convex bodies, a new and comparatively short proof of an integral-geometric kinematic formula for curvature measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02413869
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    Paper (German National Licenses)
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