On Lp-Affine Surface Area and Curvature Measures

Zhao, Yiming

doi:10.1093/imrn/rnv178

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On L_p-Affine Surface Area and Curvature Measures

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Abstract

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 Schütt and Werner's.

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On L_p-Affine Surface Area and Curvature Measures

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On L_p-Affine Surface Area and Curvature Measures