Outputs (2)

The Cheeger constant of simply connected, solvable Lie groups (2004)
Journal Article
Peyerimhoff, N., & Samiou, E. (2004). The Cheeger constant of simply connected, solvable Lie groups. Proceedings of the American Mathematical Society, 132(5), 1525-1529

We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group G with Lie algebra g is h(G) = max tr(ad(H)), where the maximum is taken over all vectors H in g with norm one.

Integrated density of states for random metrics on manifolds (2004)
Journal Article
Lenz, D., Peyerimhoff, N., & Veselic, I. (2004). Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society, 88(3), 733-752. https://doi.org/10.1112/s0024611503014576

This paper carries over the fundamental properties of random Schroedinger operators to random Laplace-Beltrami operators, that is, Laplacians with random metrics. Namely, we (A) discuss a framework for ergodic, random operators on covering manifolds... Read More about Integrated density of states for random metrics on manifolds.