Professor Norbert Peyerimhoff's Outputs (3)

Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane (2002)
Journal Article
Karp, L., & Peyerimhoff, N. (2002). Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane. Archiv der Mathematik, 79, 223-231. https://doi.org/10.1007/s00013-002-8308-z

We prove that amongst all hyperbolic triangles of equal perimeter or quadrilaterals in a given geodesic ball the regular polygon is the unique minimum for the first Dirichlet eigenvalue. Moreover, we give a geometric description of the set of all hyp... Read More about Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane.

Simplices of maximal volume or minimal total edge length in hyperbolic space (2002)
Journal Article
Peyerimhoff, N. (2002). Simplices of maximal volume or minimal total edge length in hyperbolic space. Journal of the London Mathematical Society, 66(3), 753-768. https://doi.org/10.1112/s0024610702003629

This article is mainly concerned with simplices in n-dimensional hyperbolic space. The main tool is a hyperbolic version of Steiner symmetrization. Our main results are: (A) Let T be the set of all hyperbolic n-simplices in a given closed ball B. A s... Read More about Simplices of maximal volume or minimal total edge length in hyperbolic space.

Integrated density of states for ergodic random Schrödinger operators on manifolds (2002)
Journal Article
Peyerimhoff, N., & Veselić, I. (2002). Integrated density of states for ergodic random Schrödinger operators on manifolds. Geometriae Dedicata, 91(1), 117-135. https://doi.org/10.1023/a%3A1016222913877

We consider the Riemannian universal covering of a compact manifold M = X/Γ and assume that Γ is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrödinger operators on X.