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Mixed Hessian inequalities and uniqueness in the class \(\mathcal {E}(X,\omega ,m)\)

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Abstract

We prove a general inequality for mixed Hessian measures by global arguments. Our method also yields a simplification for the case of complex Monge–Ampère equation. Exploiting this and using Kołodziej’s mass concentration technique we also prove the uniqueness of the solutions to the complex Hessian equation on compact Kähler manifolds in the case of probability measures vanishing on \(m\)-polar sets.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Jagiellonian University, Lojasiewicza 6, 30-348, Kraków, Poland

    Sławomir Dinew

  2. Mathematical Sciences, Chalmers University of Technology, 412 96, Gothenburg, Sweden

    Chinh H. Lu

Authors
  1. Sławomir Dinew
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  2. Chinh H. Lu
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Corresponding author

Correspondence to Chinh H. Lu.

Additional information

Sławomir Dinew is partially supported by NCN Grant 2013/08/A/ST1/00312. Chinh H. Lu is supported by the European Research Councils and partially supported by the french ANR project MACK.

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Dinew, S., Lu, C.H. Mixed Hessian inequalities and uniqueness in the class \(\mathcal {E}(X,\omega ,m)\) . Math. Z. 279, 753–766 (2015). https://doi.org/10.1007/s00209-014-1392-5

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  • DOI: https://doi.org/10.1007/s00209-014-1392-5

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