Hessian equations on closed Hermitian manifolds
By Dekai Zhang. 2015
66 citations recorded by the source corpus.
In this paper, using the technical tools in \cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the K\"ahler case results in \cite{HMW} and \cite{DK}.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/90fb7dc804ca2a1427cfdd81b5cce1cfc2ad0da1
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In Applied Mathematics
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- Duong H. Phong
- B. Weinkove
- Dat T. To
- Sebastien Picard
- Xiangwen Zhang
- Jian Song
In Geometry and Topology
- G'abor Sz'ekelyhidi
- Valentino Tosatti
- Duong H. Phong
- B. Weinkove
- Dat T. To
- Sebastien Picard
- Xiangwen Zhang
- Jian Song
Citations in the corpus
- Gauduchon metrics with prescribed volume form (2015, background): “of work on fully non-linear second order elliptic equations, going back to the work of Caffarelli-Nirenberg-Spruck [3] on the Dirichlet problem on domains in Rn. Some other works on this topic include [6, 7, 14, 15, 16, 17, 23, 24, 25, 27, 28, 32, 33, 41, 42, 44, 45, 46]. 1After this paper was posted”
- A second order estimate for general complex Hessian equations (2015, methodology): “1708 DUONG H. PHONG, SEBASTIEN PICARD AND XIANGWEN ZHANG Acknowledgements The authors would like to thank Pengfei Guan for stimulating conversations and for sharing his unpublished notes.”
- Fully non-linear parabolic equations on compact Hermitian manifolds (2017, background): “ for C2 estimates that we discussed in §2. A general existence result on compact Hermitian manifolds was recently obtained by Dinew and Kolodziej [10], Sun [47], and Sz´ekelyhidi [50]. See also Zhang [66]. Again, we can derive this theorem as a corollary of Theorem 1: Corollary 4 Let (X,α) be a comp”