Weak solutions of complex Hessian equations on compact Hermitian manifolds. (9th September 2016)

• Record Type: Journal Article
• Authors: Kołodziej, Sławomir; Nguyen, Ngoc Cuong
• Is Part Of: Compositio mathematica. Volume 152:Number 11(2016)
• Page Start: 2221
• Page End: 2248
• Publication Date: 2016-09-09
• Subjects: 53C55, -- 35J96, -- 32U40 (primary); weak solutions, -- complex Hessian equation, -- comparison principle; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007417
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : 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.