scholarly journals Local gradient estimates of solutions to some conformally invariant fully nonlinear equations

2006 ◽  
Vol 343 (4) ◽  
pp. 249-252 ◽  
Author(s):  
YanYan Li
Keyword(s):  
Nonlinear Equations ◽  
Gradient Estimates ◽  
Fully Nonlinear Equations ◽  
Fully Nonlinear ◽  
Estimates Of Solutions ◽  
Conformally Invariant ◽  
Local Gradient

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 Class of Fully Nonlinear Equations Arising in Conformal Geometry

2020 ◽  
Author(s):  
Li Chen ◽  
Xi Guo ◽  
Yan He
Keyword(s):  
Nonlinear Equations ◽  
Riemannian Manifolds ◽  
Existence Result ◽  
Conformal Geometry ◽  
Fully Nonlinear Equations ◽  
Fully Nonlinear ◽  
Yamabe Equation ◽  
Local Gradient

Abstract In this paper, we consider the equations of Krylov type in conformal geometry on closed smooth Riemannian manifolds, which can be viewed as an extension of $\sigma _k$-Yamabe equation. Moreover, we prove local gradient and 2nd-derivative estimates for solutions to these equations and establish an existence result.

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