The noncompact hyperbolic 3-manifold of minimal volume

Abstract

We utilize maximal cusp volumes in order to prove that the Gieseking manifold is the unique complete noncompact 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>-manifold of minimal hyperbolic volume.