Geometric analysis of metric spaces is a vibrant research area at the interface of analysis, geometry and topology. It examines the intrinsic structure of spaces endowed with a notion of distance, ...

This is a preview. Log in through your library . Abstract We show that for any hyperbolic metric on a closed 3-manifold, there exists a neighborhood such that every solution of a normalized cross ...

It is known that the j˜-metric, the half-Apollonian metric, and the scale-invariant Cassinian metric are not Gromov hyperbolic. These metrics are defined as a supremum of one-point metrics (i.e., ...

Hyperbolic geometry originated in the 19th century, when mathematicians questioned the necessity of the parallel postulate in Euclidean geometry and discovered the hyperbolic plane ℍ², which satisfied ...

The two main themes of my research are geometric group theory and analysis on metric spaces. Geometric group theory involves the study of infinite, finitely generated groups by considering how they ...