On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds
We investigate Monge-Ampère type equations on almost Hermitian manifolds and show an \(a\) \(priori\) \(L^\infty\) estimate for a smooth solution of these equations.
L. Chen, “Hessian equations of Krylov type on Kähler manifolds”, preprint, arXiv:2107.12035v3, 2021.
J. Chu, V. Tosatti and B. Weinkove, “The Monge-Ampère equation for non-integrable almost complex structures”, J. Eur. Math. Soc., vol. 21, no. 7, pp. 1949–1984, 2019.
P. Gauduchon, “Le théorème de l’excentricité nulle”, C. R. Acad. Sci. Paris S ́er. A-B, vol. 285, no. 5, pp. A387–A390, 1977.
A. Newlander and L. Nirenberg, “Complex analytic coordinates in almost complex manifolds”, Ann. of Math. (2), vol. 65, pp. 391–404, 1957.
W. Sun, “On a class of fully nonlinear elliptic equations on closed Hermitian manifolds”, J. Geom. Anal., vol. 26, no. 3, pp. 2459–2473, 2016.
W. Sun, “On a class of fully nonlinear elliptic equations on closed Hermitian manifolds II: L∞ estimate”, Comm. Pure Appl. Math., vol. 70, no. 1, pp. 172–199, 2017.
V. Tosatti and B. Weinkove, “Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds”, Asian J. Math., vol. 14, pp. 19–40, 2010.
V. Tosatti and B. Weinkove, “The complex Monge-Ampère equation on compact Hermitian manifolds”, J. Amer. Math. Soc., vol. 23, pp. 1187–1195, 2010.
Q. Tu and N. Xiang, “The Dirichlet problem for mixed Hessian equations on Hermitian manifolds”, preprint, arXiv:2201.05030v1, 2022.
L. Vezzoni, “On Hermitian curvature flow on almost complex manifolds”, Differential Geom. Appl., vol. 29, no. 5, pp. 709–722, 2011.
C.-J. Yu, “Nonpositively curved almost Hermitian metrics on products of compact almost complex manifolds”, Acta Math. Sin., vol. 31, no. 1, pp. 61–70, 2015.
J. Zhang, “Monge-Ampère type equations on almost Hermitian manifolds”, preprint, arXiv:2101.00380, 2022.
T. Zheng, “An almost complex Chern-Ricci flow”, J. Geom. Anal., vol. 28, no. 3, pp. 2129– 2165, 2018.
Copyright (c) 2022 M. Kawamura
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Japan Society for the Promotion of Science
Grant numbers JP21K13798