# G. Christopher Hruska

 G. Christopher Hruska Ph.D. (2002) Cornell University

### First Position

NSF Postdoctoral Research Fellow at the University of Chicago

### Dissertation

Nonpositively Curved Spaces with Isolated Flats

Abstract: The mildest way that a nonpositively curved space can fail to be negatively curved is for it to contain only a sparse collection of isolated flat Euclidean subspaces. The concept of a CAT(0) space whose flat planes are isolated is implicit in work of Michael Kapovich and Bernhard Leeb and of Daniel Wise and has also been studied by Bruce Kleiner. In this dissertation we introduce the Isolated Flats Property, which makes this notion explicit, and we show that several important results about Mikhail Gromov's $\delta$-hyperbolic spaces extend to the class of CAT(0) spaces with this property.
groups which act on 2-dimensional complexes with the Isolated Flats Property as well as all geometrically finite subgroups of $\Isom ( \Hyp^n )$. We also show that for each such group there is a well-defined notion of a boundary at infinity and an intrinsic notion of a subgroup being quasiconvex. These results were established by Gromov in the negatively curved setting and do not extend to general nonpositively curved spaces.