A second order estimate for complex Hessian equations on a compact Kähler manifold

By Z. Hou, Xinan Ma, Damin Wu. 2010

156 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b33e14d1af84aafc76adeda03218c09740f49906

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On a class of fully nonlinear elliptic equations on Hermitian manifolds (2013, unknown): “8) ω =ψχ u ∧ ω on closed Kähler manifolds which is consequently solvable due to the earlier work of Hou, Ma and Wu [24].”
Degenerate complex Hessian equations on compact K\"ahler manifolds (2014, methodology): “Another effort from Hou-Ma-Wu [24] provided an a priori almost C(2)-estimate without any curvature assumption.”
$$C^{2,\alpha }$$C2,α estimates for nonlinear elliptic equations in complex and almost complex geometry (2014, unknown): “The complexHessian equations (1.4)withχ = ωKählerwere solved byDinew–Kołodziej [18], who made use of estimates of Hou [34] and Hou–Ma–Wu [35].”
A priori estimates for complex Hessian equations (2011, methodology): “and consider the Hessian equation on a compact Kähler manifold X , as in [Hou 2009; Hou et al. 2010; Dinew and Kołodziej 2012]:”
Fully non-linear elliptic equations on compact Hermitian manifolds (2015, methodology): “Our calculation will mostly follow that of Hou-Ma-Wu [22] which in turn is based on ideas in Chou-Wang [5].”
The global curvature estimate for the n-2 Hessian equation (2020, methodology): “C2 estimates for the complex Hessian equations defined on Kähler manifolds have been obtain by Hou-Ma-Wu [27].”
Fully non-linear parabolic equations on compact Hermitian manifolds (2017, methodology): “The original strategy goes back to the work of Chou-Wang [6], with adaptation to complex Hessian equations by Hou-Ma-Wu [25], and to fully non-linear elliptic equations admitting a C-subsolution by Guan [19] and Székelyhidi [50].”
Fu–Yau Hessian equations (2018, background): “J. Wang [6], Hou-Ma-Wu [16], Guan [14], and the authors [22].”
The Neumann Problem for Hessian Equations (2015, methodology): “See [29] for these inequalities, one can also see [18] for the first inequality.”
A second order estimate for general complex Hessian equations (2015, methodology): “In particular, as a crucial step in the continuity method, C2 estimates for complex Hessian type equations have been studied in various settings; see [Hou et al. 2010; Sun 2014; Székelyhidi 2015; Székelyhidi et al. 2015; Zhang 2015].”
Hölder Continuous Solutions to Complex Hessian Equations (2013, background): “A major progress has been done recently both for domains in C (see [2, 9, 20]), and on compact Kähler manifolds, (see [10, 17]).”
Gauduchon metrics with prescribed volume form (2015, methodology): “We remark that an estimate of this form was proved in the context of the complex Hessian equations by Hou-Ma-Wu [19], making use of ideas of Chou-Wang [5].”
The Monge-Ampère equation for (n − 1)-plurisubharmonic functions on a compact Kähler manifold (2013, methodology): “11) (ω + √ −1∂∂u) ∧ ω = eω, for fixed 2 6 k 6 n− 1, was proved by Dinew-Ko lodziej [11], who used the second order estimate of Hou-Ma-Wu [31] (see also [3, 10, 30, 32, 33, 34, 36, 39, 59] for earlier and related work on these equations).”