scholarly journals Stability and regularity of solutions of the Monge–Ampère equation on Hermitian manifolds

2019 ◽  
Vol 346 ◽  
pp. 264-304 ◽  
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Regularity Of Solutions ◽  
Hermitian Manifolds ◽  
Monge Ampere

Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740002
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Stability Of Solutions ◽  
Hermitian Manifolds ◽  
Priori Estimates ◽  
Existence And Stability ◽  
Monge Ampere

In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampère equation on compact Hermitian manifolds. We indicate the differences between Kähler and non-Kähler setting. The results include a priori estimates, existence and stability of solutions.

Gradient estimates for Monge–Ampère type equations on compact almost Hermitian manifolds with boundary

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Masaya Kawamura
Keyword(s):  
Nonlinear Equations ◽  
Smooth Solution ◽  
A Priori ◽  
Gradient Estimates ◽  
Manifolds With Boundary ◽  
Fully Nonlinear Equations ◽  
Fully Nonlinear ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Monge Ampere

Abstract We investigate Monge–Ampère type fully nonlinear equations on compact almost Hermitian manifolds with boundary and show a priori gradient estimates for a smooth solution of these equations.

scholarly journals A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

2017 ◽  
Vol 2019 (17) ◽  
pp. 5497-5538 ◽  
Author(s):  
Tao Zheng
Keyword(s):  
Smooth Function ◽  
Existence And Uniqueness ◽  
Type Equation ◽  
Uniqueness Of Solution ◽  
Long Time Existence ◽  
Hermitian Manifolds ◽  
Long Time ◽  
Monge Ampere ◽  
Time Existence

Abstract We prove the long time existence and uniqueness of solution to a parabolic Monge–Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t$ approaches infinity which, up to scaling, is the solution to a Monge–Ampère type equation. This gives a parabolic proof of the Gauduchon conjecture based on the solution of Székelyhidi, Tosatti, and Weinkove to this conjecture.

scholarly journals C1,α regularity of solutions to parabolic Monge-Ampére equations

2012 ◽  
Vol 134 (4) ◽  
pp. 1051-1087 ◽  
Author(s):  
Panagiota Daskalopoulos ◽  
Ovidiu Savin
Keyword(s):  
Regularity Of Solutions ◽  
Monge Ampere
Sign in / Sign up

Export Citation Format

Share Document