The Christofel‐Minkowski problem III: Existence and convexity of admissible solutions

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A microscopic convexity principle for nonlinear partial differential equations (2008, methodology): “The microscopic convexity principle has been validated for a variety of fully nonlinear differential equations involving the second fundamental form of hypersurfaces ([17, 16, 18, 8]).”
A constant rank theorem for solutions of fully nonlinear elliptic equations (2007, background): “We remark that the major difference of the above proof and the proofs in [7, 11, 12, 13, 15] is the choice of the test function φ in (2.”
A class of curvature type equations. (2019, background): “The following uniqueness result was proved in [25].”