publication . Article . Preprint . 2015

On Lp-Affine Surface Area and Curvature Measures

Yiming Zhao;
Open Access
  • Published: 17 Sep 2015 Journal: International Mathematics Research Notices, volume 2,016, pages 1,387-1,423 (issn: 1073-7928, eissn: 1687-0247, Copyright policy)
  • Publisher: Oxford University Press (OUP)
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 Sch\"utt & Werner's.
Subjects
arXiv: Mathematics::Metric Geometry
free text keywords: General Mathematics, Mathematics - Metric Geometry, 52A40, Polar, Discrete mathematics, Curvature, Mathematical proof, Mathematics, Equivalence (measure theory), Affine transformation
Related Organizations
Funded by
NSF| Isoperimetric Inequalities
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1312181
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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