Mathematische Zeitschrift

, Volume 279, Issue 3–4, pp 753–766 | Cite as

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

  • Sławomir Dinew
  • Chinh H. LuEmail author


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.


Subharmonic Function Plurisubharmonic Function Positive Radon Measure Hessian Equation Pluripotential Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Mathematical SciencesChalmers University of TechnologyGothenburgSweden

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