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Mathematics > Metric Geometry

arXiv:1410.7033 (math)
[Submitted on 26 Oct 2014]

Title:Valuations and Surface Area Measures

Authors:Christoph Haberl, Lukas Parapatits
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Abstract:We consider valuations defined on polytopes containing the origin which have measures on the sphere as values. We show that the classical surface area measure is essentially the only such valuation which is SL(n) contravariant of degree one. Moreover, for all real $p$, an $L_p$ version of the above result is established for GL(n) contravariant valuations of degree $p$. This provides a characterization of the $L_p$ surface area measures from the $L_p$ Brunn-Minkowski theory.
Subjects: Metric Geometry (math.MG)
MSC classes: 52B45, 28A10
Cite as: arXiv:1410.7033 [math.MG]
  (or arXiv:1410.7033v1 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.1410.7033
Journal reference: J. Reine Angew. Math. 687 (2014), 225-245

Submission history

From: Lukas Parapatits [view email]
[v1] Sun, 26 Oct 2014 14:31:03 UTC (17 KB)
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