Gromov's minimal volume conjecture for finite-volume hyperbolic manifolds
Gromov's minimal volume conjecture for finite-volume hyperbolic manifolds
Let be a complete hyperbolic manifold with finite volume, where is a hyperbolic metric on . The minimal volume of is denoted by
Gromov's conjecture. For every complete hyperbolic manifold of finite volume,
This conjecture proposes that the hyperbolic metric realizes the minimal volume among metrics with sectional curvature bounded in absolute value by . The supplied source does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
E. Costa, R. Diógenes and E. Ribeiro, “Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds”, arXiv:1407.8137 (2015).
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