On L_p affine surface area and curvature measures

Yiming Zhao New York University

Convex and Discrete Geometry mathscidoc:1703.40009

Int. Math. Res. Not. IMRN, (5), 1387-1423, 2016
The relationship between Lp affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of Lp 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 Schutt & Werner’s.
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  title={On L_p affine surface area and curvature measures},
  author={Yiming Zhao},
  booktitle={Int. Math. Res. Not. IMRN},
Yiming Zhao. On L_p affine surface area and curvature measures. 2016. In Int. Math. Res. Not. IMRN. pp.1387-1423. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170302052127014373588.
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