A class of fully nonlinear equations arising from conformal geometry

By W. Sheng, Yan Zhang. 2006

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The Neumann Problem for Hessian Equations (2015, methodology): “tudied by Y.Y.Li [22], Urbas [44] and Guan [13]. In recent years the Hessian type equation also appears in conformal geometry, which started from Chang-Gursky-Yang [5] and the related development by ([16], [23], [17], [36],[10]). In Kahler geometry, the Hessian equation was studied by Hou-Ma-Wu [18]”
On Harnack inequalities and singularities of admissible metrics in the Yamabe problem (2005, background): “By the a priori estimates in [13] and the comparison principle, the solution of (4.”
The Yamabe problem for higher order curvatures (2005, background): “Lemma 3.1. [ GW1 ] Let u ∈ C3 be a k-admissible positive solution of (3.1) in a geodesic”
Complete Conformal Metrics of Negative Ricci Curvature on Compact Manifolds with Boundary (2008, background): “In [11] Pengfei Guan and Guofang Wang proved a remarkable local gradient estimate which, unlike Theorem 2.”
Recent developments in elliptic partial differential equations of Monge-Ampere type (2006, methodology): “The following theorem, due to Sheng, Trudinger and Wang [26] (k ≤ n/2), Gursky and Viaclovsky [16] (k > n/2) concerns the solvability of the higher order Yamabe problem, k > 1.”
Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds (2014, background): “Following [25] we choose a cutoff function ζ ∈ C 0 (Br) such that (4.”