Journal ArticleDOI
Local estimates for a class of fully nonlinear equations arising from conformal geometry
Pengfei Guan,Guofang Wang +1 more
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This article is published in International Mathematics Research Notices.The article was published on 2003-01-01. It has received 160 citations till now. The article focuses on the topics: Conformal geometry & Nonlinear system.read more
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On some conformally invariant fully nonlinear equations
Aobing Li,Yanyan Li +1 more
TL;DR: In this paper, Liouville type theorems, Harnack type inequalities, existence and compactness of solutions to some nonlinear version of the Yamabe problem are discussed. But these results are not applicable to the Niren-Berg problem.
Journal ArticleDOI
A fully nonlinear conformal flow on locally conformally flat manifolds
Pengfei Guan,Guofang Wang +1 more
TL;DR: In this paper, the authors studied the σk-Yamabe problem for locally conformal flat manifolds when k = n/2 and proved the long-time existence and the sequential convergence of flow.
Journal ArticleDOI
A second order estimate for complex Hessian equations on a compact Kähler manifold
Zuoliang Hou,Xi-Nan Ma,Damin Wu +2 more
Journal ArticleDOI
The Yamabe problem for higher order curvatures
TL;DR: In this paper, the authors proved the solvability of the k-Yamabe problem in the remaining cases k ≤ n/2, under the hypothesis that the problem is variational.
Journal ArticleDOI
Second-order estimates and regularity for fully nonlinear elliptic equations on riemannian manifolds
TL;DR: In this paper, a priori second-order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under structure conditions which are close to optimal were derived.
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Journal ArticleDOI
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
TL;DR: On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂ Ω as discussed by the authors.
Journal Article
Remarks concerning the conformal deformation of riemannian structures on compact manifolds
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.
Book ChapterDOI
Variational theory for the total scalar curvature functional for riemannian metrics and related topics
Journal ArticleDOI
Boundedly nonhomogeneous elliptic and parabolic equations in a domain
TL;DR: In this article, the first boundary value problem for equations of the form, where and are positive homogeneous functions of the first degree in, convex upwards in, that satisfy a uniform strict ellipticity condition is proved.