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The Lp-Minkowski problem for −n < p < 1

Advances in Mathematics (2019) 341 493-535
DOI: 10.1016/j.aim.2018.10.032
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Abstract

Chou and Wang's existence result for the Lp-Minkowski problem on Sn−1 for p∈(−n,1) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p∈(0,1).

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Bianchi, G., Böröczky, K. J., Colesanti, A., & Yang, D. (2019). The Lp-Minkowski problem for −n < p < 1. Advances in Mathematics, 341, 493–535. https://doi.org/10.1016/j.aim.2018.10.032

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