We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results are proved via rearrangement techniques.
On the non-existence of compact surfaces of genus one with prescribed, almost constant mean curvature, close to the singular limit
On the shape of compact hypersurfaces with almost constant mean curvature
$f$-extremal domains in hyperbolic space
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