A constant rank theorem for solutions of fully nonlinear elliptic equations

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Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space (2013, methodology): “The constant rank theorem was initiated by Caffarelli-Friedman [10] and Korevaar-Lewis [32] for semilinear elliptic equations and developed by Guan-Ma [27], Caffarelli-Guan-Ma [9] and Bian-Guan [3] for fully nonlinear elliptic equations.”
The Existence of Convex Body with Prescribed Curvature Measures (2009, background): “2 in [4], it relies on the following deformation lemma.”
A microscopic convexity principle for nonlinear partial differential equations (2008, unknown): “There have been significant development of analysis techniques in literature [7, 27, 17, 16, 18, 8] for this purpose, in particular the method introduced in [8].”