The k-Hessian Equation

By Xu-jia Wang. 2009

202 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/29ea3d724fd7d491e0b36e186813e69d7d3a6884

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A second order estimate for complex Hessian equations on a compact Kähler manifold (2010, unknown): “Wang [14] and the references therein.”
The Neumann Problem for Hessian Equations (2015, methodology): “For more details please see the survey paper by Wang [31].”
A second order estimate for general complex Hessian equations (2015, background): “The real counterparts of (1-2) for 1< k ≤ n, with ψ not depending on the gradient of u, have been studied extensively in the literature (see the survey paper [Wang 2009] and more recent related work [Guan 2014]), as these equations appear naturally and play very important roles in both classical and”
Liouville and Calabi-Yau type theorems for complex Hessian equations (2012, background): “ of the complex Hessian matrix of a real valued function - the elementary symmetric polynomials of its eigenvalues. Its real counterpart has numerous applications and has been thoroughly studied (see [W]). Some equations of similar type appear in the study of geometric deformation ﬂows such as the J”
The global curvature estimate for the n-2 Hessian equation (2020, background): “More details about the proof of these formulas can be found in [28] and [49].”
Complete Conformal Metrics of Negative Ricci Curvature on Compact Manifolds with Boundary (2008, background): “We instead refer the reader to the lecture notes and exploration articles [4], [10] [17], [27], [29], and references therein.”
Degenerate complex Hessian equations on compact K\"ahler manifolds (2014, background): “For a survey of this theory we refer the reader to [39], [40], [45], [13] and the references therein.”
A priori estimates for complex Hessian equations (2011, background): “(3) [Wang 2009]: Let Sk;i (λ) := Sk(λ)λi=0 = ∂Sk+1 ∂ λi (λ).”