Open AccessThe mean curvature estimate for the level sets of solutions of the 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 - 10.1088/1742-6596/1941/1/012062
Subject(s) - mathematics , monge–ampère equation , riemannian manifold , mathematical analysis , curvature , ricci curvature , dirichlet problem , mean curvature , manifold (fluid mechanics) , sectional curvature , scalar curvature , function (biology) , boundary value problem , geometry , mechanical engineering , evolutionary biology , engineering , biology
For the fully nonlinear elliptic Monge-Ampere equation det D 2 u = 1 with homogeneous Dirichlet boundary value condition, in this paper, a function related to the curvature of the level set of the solution was established, then the differential inequality of the strictly convex solutions of the equation on four-dimensional Riemannian manifold was got. The maximum value of the auxiliary function at the boundary was obtained by using the maximum principle and the mean curvature estimation for the level sets of the solution was given.