Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
From MaRDI portal
Publication:609471
DOI10.4310/AJM.2010.v14.n1.a3zbMath1208.32034arXiv0909.4496MaRDI QIDQ609471
Valentino Tosatti, Ben Weinkove
Publication date: 1 December 2010
Published in: The Asian Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0909.4496
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Calabi-Yau theory (complex-analytic aspects) (32Q25) Complex Monge-Ampère operators (32W20)
Related Items
On uniform estimate of complex elliptic equations on closed Hermitian manifolds ⋮ Pluripotential theory on compact Hermitian manifolds ⋮ The complex Monge-Ampère equation on compact Hermitian manifolds ⋮ GEOMETRY OF HERMITIAN MANIFOLDS ⋮ On the \(J\)-flow in Sasakian manifolds ⋮ On a class of fully nonlinear elliptic equations on closed Hermitian manifolds ⋮ Complex Monge-Ampère equations and totally real submanifolds ⋮ The continuity equation of the Gauduchon metrics ⋮ The complex Monge-Ampère type equation on compact Hermitian manifolds and applications ⋮ The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds ⋮ Mabuchi and Aubin-Yau functionals over complex surfaces ⋮ The \(C^0\) estimate for the quaternionic Calabi conjecture ⋮ Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds ⋮ Gradient and Hessian estimates for the Hermitian Monge-Ampère equation ⋮ The parabolic flows for complex quotient equations ⋮ On a Class of Fully Nonlinear Elliptic Equations on Closed Hermitian Manifolds II:L∞Estimate ⋮ The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold ⋮ Quasi-plurisubharmonic envelopes 3: solving Monge-Ampère equations on Hermitian manifolds ⋮ Hessian equations of Krylov type on Kähler manifolds ⋮ A \(C^0\) \textit{a priori} estimate for the quaternionic Monge-Ampère equation in almost hyperhermitian geometry ⋮ Fully non-linear elliptic equations on compact almost Hermitian manifolds ⋮ On the Alesker-Verbitsky conjecture on hyperKähler manifolds ⋮ Regularity estimates of solutions to complex Monge-Ampère equations on Hermitian manifolds ⋮ Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds ⋮ The Dirichlet problem for a complex Monge-Ampère type equation on Hermitian manifolds ⋮ A note on the deformed Hermitian Yang-Mills PDE ⋮ An almost complex Chern-Ricci flow ⋮ Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms ⋮ Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds ⋮ A numerical criterion for generalised Monge-Ampère equations on projective manifolds ⋮ \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry ⋮ On a class of fully nonlinear elliptic equations on Hermitian manifolds ⋮ \(C^{1,1}\) regularity of degenerate complex Monge-Ampère equations and some applications ⋮ Fully non-linear degenerate elliptic equations in complex geometry ⋮ The parabolic Monge-Ampère equation on compact almost Hermitian manifolds ⋮ A parabolic flow of balanced metrics ⋮ On the non-existence of static pluriclosed metrics on non-Kähler minimal complex surfaces ⋮ Unnamed Item ⋮ A class of the non-degenerate complex quotient equations on compact Kähler manifolds ⋮ The Calabi–Yau equation on 4-manifolds over 2-tori ⋮ The Monge-Ampère equation for non-integrable almost complex structures ⋮ A priori estimates for a generalized Monge–Ampère PDE on some compact Kähler manifolds ⋮ Regularizing properties of complex Monge-Ampère flows. II: Hermitian manifolds ⋮ A priori estimates for Donaldson's equation over compact Hermitian manifolds ⋮ Parabolic complex Monge-Ampère type equations on closed Hermitian manifolds ⋮ Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kähler manifolds ⋮ The continuity equation, Hermitian metrics and elliptic bundles ⋮ On the uniform estimate in the Calabi-Yau theorem. II ⋮ Plurisubharmonic functions and nef classes on complex manifolds ⋮ Hermitian metrics, \((n-1,n-1)\) forms and Monge-Ampère equations ⋮ A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics ⋮ Hessian equations of Krylov type on compact Hermitian manifolds ⋮ \(C^{2,\alpha}\) regularities and estimates for nonlinear elliptic and parabolic equations in geometry