Dihedral rigidity in hyperbolic 3-space

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="negative 6"> <mml:semantics> <mml:mrow> <mml:mo> − </mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">-6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -space.