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Sharp convex Lorentz–Sobolev inequalities

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Abstract

New sharp Lorentz–Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the L p Minkowski problem. New L p isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz–Sobolev inequalities are analytic analogues of isocapacitary and isoperimetric inequalities.

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Authors and Affiliations

  1. Department of Mathematics, Polytechnic Institute of NYU, 6 MetroTech Center, Brooklyn, NY, 11201, USA

    Monika Ludwig & Gaoyong Zhang

  2. Department of Mathematics and Statistics, Memorial University, St. John’s, NL, A1C 5S7, Canada

    Jie Xiao

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  1. Monika Ludwig
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  2. Jie Xiao
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  3. Gaoyong Zhang
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Correspondence to Jie Xiao.

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Ludwig, M., Xiao, J. & Zhang, G. Sharp convex Lorentz–Sobolev inequalities. Math. Ann. 350, 169–197 (2011). https://doi.org/10.1007/s00208-010-0555-x

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