Degenerate complex Hessian equations on compact K\"ahler manifolds
By Chinh H. Lu, Van-Dong Nguyen. 2014
54 citations recorded by the source corpus.
Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $m\in \mathbb{N}$ such that $1\leq m \leq n$. We prove that any $(\omega,m)$-sh function can be approximated from above by smooth $(\omega,m)$-sh functions. A potential theory for the complex Hessian equation is also developed which generalizes the classical pluripotential theory on compact K\"ahler manifolds. We then use novel variational tools due to Berman, Boucksom, Guedj and Zeriahi to study degenerate complex Hessian equations.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a95f7dbb0be95d082dcbce3f853cfd2c42c4a826
How researchers see this paper
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In Applied Mathematics
- Tam'as Darvas
- Sebastien Picard
- Duong H. Phong
- Xiangwen Zhang
- Robert J. Berman
- B. Weinkove
- Chi Li
- Valentino Tosatti
In Geometry and Topology
- Tam'as Darvas
- Duong H. Phong
- Xiangwen Zhang
- Sebastien Picard
- Robert J. Berman
- B. Weinkove
- Chi Li
- Valentino Tosatti
Citations in the corpus
- A second order estimate for general complex Hessian equations (2015, background): “The corresponding problem on compact Kähler or Hermitian manifolds has also been studied extensively; see, for example, [Dinew and Kołodziej 2014; Hou 2009; Kołodziej and Nguyen 2016; Lu and Nguyen 2015; Zhang 2010].”
- Geometric pluripotential theory on Kähler manifolds (2019, methodology): “In our approach we will follow closely the simplified argument proposed by Lu and Nguyen [85].”