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The \(p\)-Affine Capacity

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Abstract

In this paper, the \(p\)-affine capacity is introduced for \(1<p<n\) and then developed to discover the upper and lower isocapacitary inequalities that strengthen optimally both the Maz’ya \(p\)-isocapacitary inequality and the Lutwak–Yang–Zhang \(L_p\) affine isoperimetric inequality over the \(n\)-dimensional Euclidean space \({\mathbb {R}}^{n}\).

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Acknowledgments

The author wishes to thank the referee for useful comments on this paper. Research supported in part by NSERC and URP of MUN, Canada.

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

    Jie Xiao

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  1. Jie Xiao
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Correspondence to Jie Xiao.

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Xiao, J. The \(p\)-Affine Capacity. J Geom Anal 26, 947–966 (2016). https://doi.org/10.1007/s12220-015-9579-5

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  • DOI: https://doi.org/10.1007/s12220-015-9579-5

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