Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary.
Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
Singularity structure in mean curvature flow of mean-convex sets.
An isoperimetric comparison theorem.
Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
Hyperbolic groups with low-dimensional boundary
Inverse Limit Spaces Satisfying a Poincaré Inequality
We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces,...
On tori without conjugate points.
Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation
We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.
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