$\mathcal{M}$-convex hypersurfaces with prescribed shifted Gaussian curvature in warped product manifolds

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

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\(\mathcal{M}\)-convex hypersurfaces with prescribed shifted Gaussian curvature in warped product manifolds