scholarly journals The complex Monge–Ampère type equation on compact Hermitian manifolds and applications

2016 ◽  
Vol 286 ◽  
pp. 240-285 ◽  
Author(s):  
Ngoc Cuong Nguyen
Keyword(s):  
Type Equation ◽  
Hermitian Manifolds ◽  
Monge Ampere

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.

Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets

2021 ◽  
Author(s):  
Le Mau Hai ◽  
Vu Van Quan
Keyword(s):  
Pseudoconvex Domain ◽  
Hölder Continuity ◽  
Type Equation ◽  
Holder Continuity ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Strictly Pseudoconvex Domain ◽  
Monge Ampere

In this paper, we establish existence of Hölder continuous solutions to the complex Monge–Ampère-type equation with measures vanishing on pluripolar subsets of a bounded strictly pseudoconvex domain [Formula: see text] in [Formula: see text].

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.

On a time-depending Monge–Ampère type equation

2012 ◽  
Vol 75 (10) ◽  
pp. 4006-4013 ◽  
Author(s):  
B. Brandolini
Keyword(s):  
Type Equation ◽  
Monge Ampere
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