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Weak solutions of complex Hessian equations on compact Hermitian manifolds
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 11 / November 2016
- Published online by Cambridge University Press:
- 09 September 2016, pp. 2221-2248
- Print publication:
- November 2016
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- Article
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We prove the existence of weak solutions of complex
$m$ -Hessian equations on compact Hermitian manifolds for the non-negative right-hand side belonging to 
$L^{p}$ , 
$p>n/m$ ( 
$n$ is the dimension of the manifold). For smooth, positive data the equation has recently been solved by Székelyhidi and Zhang. We also give a stability result for such solutions.
