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math.MG2018★ 1 cited
Coarse compactifications and controlled products
Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi
We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gro…
math.MG2017★ 23 cited
A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
Tomohiro Fukaya, Shin-ichi Oguni
We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boun…
math.MG2014
On coarse geometric aspects of the Hilbert geometry
Ryosuke Mineyama, Shin-ichi Oguni
We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is…