scholarly journals Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary

2006 ◽  
Vol 28 (4) ◽  
pp. 509-543 ◽  
Author(s):  
Qinian Jin ◽  
Aobing Li ◽  
YanYan Li
Keyword(s):  
Existence Results ◽  
Yamabe Problem ◽  
Manifolds With Boundary ◽  
Fully Nonlinear

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 The Yamabe problem on manifolds with boundary: Existence and compactness results

1999 ◽  
Vol 99 (3) ◽  
pp. 489-542 ◽  
Author(s):  
Zheng-Chao Han ◽  
Yanyan Li
Keyword(s):  
Yamabe Problem ◽  
Manifolds With Boundary

scholarly journals Counterexamples to C2 Boundary Estimates for a Fully Nonlinear Yamabe Problem on Manifolds with Boundary

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
YanYan Li ◽  
Luc Nguyen
Keyword(s):  
Mean Curvature ◽  
A Priori Estimates ◽  
A Priori ◽  
Gradient Estimates ◽  
Manifolds With Boundary ◽  
Fully Nonlinear ◽  
Priori Estimates ◽  
Hessian Estimates ◽  
The Mean ◽  
Boundary Estimates

AbstractOn closed manifolds, gradient and Hessian a priori estimates for fully nonlinear Yamabe problems are known to hold. On manifolds with boundary, gradient estimates are known to hold, while Hessian estimates hold if the prescribed mean curvature is positive. Examples are given here which show that Hessian estimates can fail when the mean curvature is negative.

scholarly journals Linear Perturbation of the Yamabe Problem on Manifolds with Boundary

2017 ◽  
Vol 28 (2) ◽  
pp. 1315-1340 ◽  
Author(s):  
Marco Ghimenti ◽  
Anna Maria Micheletti ◽  
Angela Pistoia
Keyword(s):  
Linear Perturbation ◽  
Yamabe Problem ◽  
Manifolds With Boundary
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