On $L_p$ Affine Surface Area and Curvature Measures

Preprint English OPEN
Zhao, Yiming (2015)
  • Related identifiers: doi: 10.1093/imrn/rnv178
  • Subject: 52A40 | Mathematics - Metric Geometry
    arxiv: Mathematics::Metric Geometry

The relationship between $L_p$ affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of $L_p$ affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Sch\"utt & Werner's.
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