On the partial uniform ellipticity and complete conformal metrics with prescribed curvature functions on manifolds with boundary

2020/11/17 by Yuan, Rirong
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.08580

Abstract

We consider the problem of finding complete conformal metrics with prescribed curvature functions of the Einstein tensor and of more general modified Schouten tensors. To achieve this, we reveal an algebraic structure of a wide class of fully nonlinear equations. Our method is appropriate and delicate as shown by a topological obstruction. Finally, we discuss Hessian equations and Weingarten equations by confirming a key assumption.

Related

• An extension of prescribed problems on the conformal classes of complete metrics
• Prescribed curvature tensor in locally conformally flat manifolds
• The partial uniform ellipticity and prescribed problems on the conformal classes of complete metrics
• Conformal geometry and fully nonlinear equations
• Fully nonlinear elliptic equations for some prescribed curvature problems on Hermitian manifolds