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October 8, 20250 citationsOpen Access

Asymptotic Plateau problem for 2-convex hypersurface in H⁴

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DCD ChenZSZhenan SuiLSLi Sun

Key Points

  • The main finding shows the existence of smooth complete 2-convex hypersurfaces with specific curvature conditions.
  • The key evidence proves a critical curvature equation involving three principal curvatures matches a constant's cubic relation.
  • An observational analysis explores geometry within hyperbolic space, addressing prescribed boundary conditions at infinity.
  • This research may enable further exploration in geometric analysis, potentially influencing higher-dimensional geometric theories.

Abstract

We prove the existence of smooth complete 2-convex hypersurface which satisfies prescribed curvature equation (₁ + ₂) (₁ + ₃) (₂ + ₃) = (2) ³ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where (0, 1) is a constant. We also prove the existence for ₖ (₂ + + ₙ, , ₁ + + ₍ - ₁) = Cₙᵏ (n - 1) ᵏ ᵏ with k < n in H^n + 1.

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Cite This Study

Chen et al. (2025) studied this question.

synapsesocial.com/papers/68e6d7971ffa7aa7d63d1825https://doi.org/10.48550/arxiv.2506.00565
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