Open AccessA Differential Inequality for the Solution of Monge Ampère Equation on Riemannian Manifold
Author(s) -
Xuemei Yu
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1903/1/012060
Subject(s) - mathematics , riemannian manifold , mathematical analysis , monge–ampère equation , dirichlet boundary condition , homogeneous , sectional curvature , manifold (fluid mechanics) , boundary value problem , constant (computer programming) , curvature , scalar curvature , geometry , combinatorics , mechanical engineering , programming language , computer science , engineering
In three-dimensional Riemannian manifolds with constant curvature, the elliptic Monge amp è re equation satisfying the homogeneous Dirichlet boundary value condition is studied. Under certain conditions, an estimate related to the solution of the equation is made, and a detailed proof of differential inequality is given.