Geometric analysis demonstrates the existence of constant mean curvature Killing graphs over exterior domains in hyperbolic space, highlighting broad solvability for non-compact boundary problems.
Given H∈ [0,1) H ∈ [ 0 , 1 ) and given a C⁰ C 0 exterior domain Ω Ω in a $$H-$$ H - hypersphere of Hⁿ⁺¹, H n + 1 , the existence of hyperbolic Killing graphs of CMC H defined in Ω ̄ Ω ¯ with boundary ∂ Ω ∂ Ω included in the $$H-$$ H - hypersphere is obtained.
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Klaser et al. (2026) studied this question.
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