Abstract
We give, under appropriate regularity assumptions, a strengthening of the Aleksandrov–Fenchel inequality in the form of a stability estimate.
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Aleksandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern, I: Verallgemeinerung einiger Begriffe der Theorie der konvexen Körper (in Russian). Mat. Sbornik N. S. 2, 947–972 (1937)
Bol, G.: Zur Theorie der konvexen Körper. Jahresber. Deutsche Math.-Ver. 49, 113–123 (1939)
Gardner, R.J.: Geometric Tomography. Cambridge Univ. Press, New York (1995)
Geppert, H.: Über den Brunn-Minkowskischen Satz. Math. Z. 42, 238–254 (1937)
Goodey, P.R., Groemer, H.: Stability results for first order projection bodies. Proc. Am. Math. Soc. 109, 1103–1114 (1990)
Khovanskiĭ, A.G.: Newton polyhedra and genus of complete intersections. Funktsional. Anal. i Prilozhen. 12, 51–61. Funct. Anal. Appl. 12, 38–46 (1978)
Langevin, R., Levitt, G., Rosenberg, H.: Hérissons et multihérissons (enveloppes paramétrées par leur application de Gauss). In: Singularities, Banach Center Publ. 20, Warsaw, PWN, pp. 245–253 (1988)
Martinez-Maure, Y.: De nouvelles inégalit és géométriques pour les hérissons. Arch. Math. 72, 444–453 (1999)
Martinez-Maure, Y.: Hedgehogs and zonoids. Adv. Math. 158, 1–17 (2001)
Martinez-Maure, Y.: Théorie des hérissons et polytopes. C. R. Acad. Sci. Paris Sér. I 336, 241–244 (2003)
Schneider, R.: Stability in the Aleksandrov–Fenchel–Jessen theorem. Mathematika 36, 50–59 (1989)
Schneider, R.: Convex Bodies: The Brunn–Minkowski Theory, 2nd expanded ed. Cambridge Univ. Press (2014)
Teissier, B.: Du théorème de l’index de Hodge aux inégalités isopérimétriques. C. R. Acad. Sci. Paris Sér. A-B 288, 287–289 (1979)
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Communicated by A. Constantin.
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Martinez-Maure, Y. A stability estimate for the Aleksandrov–Fenchel inequality under regularity assumptions. Monatsh Math 182, 65–76 (2017). https://doi.org/10.1007/s00605-015-0865-x
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DOI: https://doi.org/10.1007/s00605-015-0865-x