The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equation

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Hypersurfaces of prescribed curvature measure (2011, background): “This problem has been extensively studied, we refer to [12] for an updated account.”
Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “Important progress was made recently by Guan-Ma [37].”
The Christoffel-Minkowski Problem II: Weingarten Curvature Equations* (2006, methodology): “The main argument of the proof follows the one in [ 12 ], which in turn was motivated by the works of Caarelli-Friedma n [4] and Korevaar-Lewis [13].”
The Christofel‐Minkowski problem III: Existence and convexity of admissible solutions (2006, methodology): “In [15], we considered the existence of convexsolutions of the following equation: Sk(uij + uδij) = φ on S, (1.”