Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

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Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations (2009, unknown): “Many authors extended these results since then; see for instance [14, 20, 7, 26] and references therein.”
A family of degenerate elliptic operators: Maximum principle and its consequences (2016, unknown): “In the case of uniformly elliptic fully nonlinear operators, this has been proved to be the case in different context (see [3, 6, 9, 20, 24, 27]).”
Fundamental solutions of homogeneous fully nonlinear elliptic equations (2009, background): “Indeed, several of the ideas we employ in our proof of Theorem 3 are related to the principal eigenvalue theory for fully nonlinear operators developed in [20, 3, 24, 1].”
Solvability of Uniformly Elliptic Fully Nonlinear PDE (2010, unknown): “For (ii) we use in addition some recent results on existence and properties of eigenvalues of convex positively homogeneous operators, obtained in [QS1].”
Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations (2008, background): “See Section 6 for some nonexistence results, and Sirakov [34] for much more on the failure of existence and uniqueness of solutions of (2.6), for λ between the two half-eigenvalues.”