We show that the flow on a Bers slice given by the Weil-Petersson gradient vector field of renormalized volume is globally attracting to its fuchsian basepoint.
We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality for 2-spheres with pinched curvature; this allows us to improve our bound on the length of the shortest closed geodesic in the pinched curvature setting.
Let π be a hyperbolic 3-manifold with no rank two cusps admitting an embedding in π 3 . Then, if π admits an exhaustion by π 1 -injective sub-manifolds there exists Cantor sets πΆ π β π 3 such that π π = π 3 ⧡ πΆ π is hyperbolic and π π β π geometrically.M S C ( 2 0 2 0 ) 30F40 (primary)
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