This work demonstrates conditions for 2-convex hypersurfaces, establishing curvature equations in hyperbolic space, indicating potential for broader geometric applications.
We prove the existence of smooth complete $2$-convex hypersurface which satisfies prescribed curvature equation (κ₁ + κ₂)(κ₁ + κ₃)(κ₂ + κ₃) = (2 σ)³ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where σ ∈ (0, 1) is a constant. We also prove the existence for σₖ (κ₂ + ⋯ + κₙ, ⋯, κ₁ + ⋯ + κn - 1) = Cₙᵏ (n - 1)ᵏ σᵏ with $k < n$ in Hn + 1.
No takes yet. Share an insight, caveat, or question.
Chen et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: