ON THE GEOMETRY AT INFINITY OF MANIFOLDS WITH LINEAR VOLUME GROWTH AND NONNEGATIVE RICCI CURVATURE

We prove that an open noncollapsed manifold with nonnegative Ricci curvature and linear volume growth always splits off a line at infinity. This completes the final step to prove the existence of isoperimetric sets for given large volumes in the above setting. We also find that under our assumptions, the diameters of the level sets of any Busemann function are uniformly bounded as opposed to a classical result stating that they can have sublinear growth when the end is collapsing. Moreover, some equivalent characterizations of linear volume growth are given. Finally, we construct an example to show that for manifolds in our setting, although their limit spaces at infinity are always cylinders, the cross sections can be nonhomeomorphic.