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Scalar curvature, volume, and Weil-Petersson translation length
Cameron Gates Rudd
We construct metrics on pseudoAnosov mapping tori that make every fiber an intrinsically hyperbolic stable minimal surface, and which have scalar curvature identically -6. Using th…
Filling 1-cycles, 2-cycle complexity, and torsion growth
Cameron Gates Rudd
For 2-complexes with trivial first Betti number, we study quantitative connections between filling inequalities for 1-cycles, the complexity of the second homology, and the size of…
Magnetic geodesics, Hodge Laplacian eigenvalues, and isoperimetric inequalities
Cameron Gates Rudd
An isoperimetric constant relating length and stable area, or alternatively for hyperbolic manifolds, length and stable commutator length, serves as a Cheeger constant for the smal…
Property (T) and Poincaré duality in dimension three
Cameron Gates Rudd
We use a recent result of Bader and Sauer on coboundary expansion to prove residually finite three-dimensional Poincaré duality groups never have property (T). This implies such gr…