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Complex Hessian equations with prescribed singularity on compact Kahler manifolds

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 نشر من قبل Chinh Lu
 تاريخ النشر 2019
  مجال البحث
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Let $(X,omega)$ be a compact Kahler manifold of dimension $n$ and fix $1leq mleq n$. We prove that the total mass of the complex Hessian measure of $omega$-$m$-subharmonic functions is non-decreasing with respect to the singularity type. We then solve complex Hessian equations with prescribed singularity, and prove a Hodge index type inequality for positive currents.



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