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Some Affine Invariants Revisited

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Asymptotic Geometric Analysis

Part of the book series: Fields Institute Communications ((FIC,volume 68))

Abstract

We present several sharp inequalities for the SL(n) invariant Ω 2, n (K) introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. A connection arose with the Paouris-Werner invariant Ω K defined for convex bodies K whose centroid is at the origin. We offer two alternative definitions for Ω K when K ∈ C + 2. The technique employed prompts us to conjecture that any SL(n) invariant of convex bodies with continuous and positive centro-affine curvature function can be obtained as a limit of normalized p-affine surface areas of the convex body.

Mathematical Subject Classifications (2010): 52A40, 52A38, 52A20, 53A07

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Acknowledgements

I am thankful to Monika Ludwig, Vitali Milman and Nicole Tomczak-Jaegermann, the organizers of the 2010 Workshop on Asymptotic Geometric Analysis and Convexity, for the invitation to participate, to the Fields Institute for the hospitality and, to all of the above, for the stimulating atmosphere during my stay there.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, Canada, H3G 1M8

    Alina Stancu

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  1. Alina Stancu
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Correspondence to Alina Stancu .

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Editors and Affiliations

  1. TU Wien, Wiedner Hauptstrasse 8–10, Wien, 1040, Austria

    Monika Ludwig

  2. Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Schreiber Building 334, Tel Aviv, 69978, Israel

    Vitali D. Milman

  3. University of Ottawa, Ottawa, K1N 6N5, Canada

    Vladimir Pestov

  4. , Department of Math and Stat Scis, University of Alberta, Central Academic Bldg 632, Edmonton, T6G 2G1, Alberta, Canada

    Nicole Tomczak-Jaegermann

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Stancu, A. (2013). Some Affine Invariants Revisited. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_16

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