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Professor Norbert Peyerimhoff's Outputs (70)

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.

Curvature and Geometry of Tessellating Plane Graphs (2001)
Journal Article
Baues, O., & Peyerimhoff, N. (2001). Curvature and Geometry of Tessellating Plane Graphs. Discrete & Computational Geometry, 25(1), 141-159. https://doi.org/10.1007/s004540010076

We show that the growth of plane tessellations and their edge graphs may be controlled from below by upper bounds for the combinatorial curvature. Under the assumption that every geodesic path may be extended to infinity we provide explicit estimates... Read More about Curvature and Geometry of Tessellating Plane Graphs.

Spectral gaps of Schroedinger operators on hyperbolic space (2000)
Journal Article
Karp, L., & Peyerimhoff, N. (2000). Spectral gaps of Schroedinger operators on hyperbolic space. Mathematische Nachrichten, 217, 105-124

This paper is mainly concerned with estimates of spectral gaps of Schroedinger operators with smooth potential on real hyperbolic space. The estimates are obtained by explicit constructions of approximate generalized eigenfunctions. Among the results... Read More about Spectral gaps of Schroedinger operators on hyperbolic space.

On index formulas for manifolds with metric horns (1998)
Journal Article
Lesch, M., & Peyerimhoff, N. (1998). On index formulas for manifolds with metric horns. Communications in Partial Differential Equations, 23(3 & 4), 649-684

In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauss-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have unique close... Read More about On index formulas for manifolds with metric horns.

On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space (1998)
Journal Article
Karp, L., & Peyerimhoff, N. (1998). On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space. Analysis, 18, 217-225. https://doi.org/10.1524/anly.1998.18.3.217

Let H be the n-dimensional real hyperbolic space and pi: H -> M be the universal covering map of a compact Riemannian manifold M of constant curvature -1. Let P be a k-dimensional complete totally geodesic submanifold of H and P_r be the correspondin... Read More about On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space.

Mathematik in Anwendung mit C++ (1994)
Book
Huettenhofer, M., Lesch, M., & Peyerimhoff, N. (1994). Mathematik in Anwendung mit C++. Quelle & Meyer

In diesem Buch werden ausgewaehlte Themen der Mathematik dargestellt, die sich besonders gut durch Algorithmen veranschaulichen lassen. Im zahlentheoretischen Teil des Buches geht es um die Teilbarkeit ganzer Zahlen und um Primzahlen - eine Thematik,... Read More about Mathematik in Anwendung mit C++.

The del-bar-operator on algebraic curves (1990)
Journal Article
Bruening, J., Peyerimhoff, N., & Schroeder, H. (1990). The del-bar-operator on algebraic curves. Communications in Mathematical Physics, 129, 525-534. https://doi.org/10.1007/bf02097104

For a singular algebraic curve we show that all closed extensions of del-bar are Fredholm, and we give a general index formula. In particular, we prove a modified version of a conjecture due to Mac Pherson.