The 4th order terms of a Monge-Ampère solution
Abstract
In the tangent bundle of real-analytic ( M , g ) (M,g) , it is well-known that the Monge-Ampère equation ( ∂ ∂ ¯ ρ ) n = 0 , 2 i ∂ ∂ ¯ ρ | M = g (\partial \bar \partial \sqrt \rho )^n=0, \ 2i\partial \bar \partial \rho |_M=g has, in terms of normal coordinates { x j } \{x_j\} in M M , the asymptotic expansion ρ ( x + i y ) = ∑ j y j 2 + O ( 4 ) \rho (x+iy)=\sum _{j} y^2_{j} + O(4) . As far as we know, there is no further achievements on 4th order terms yet. We make them explicit in this article ρ ( x + i y ) = ∑ i y i
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 2035–2041
- Publication date
- 14 January 2026
- Language
- EN