Professor Norbert Peyerimhoff's Outputs (4)

Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature (2006)
Journal Article
Klassert, S., Lenz, D., Peyerimhoff, N., & Stollmann, P. (2006). Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature. Proceedings of the American Mathematical Society, 134(5), 1549-1559

This paper is concerned with elliptic operators on plane tessellations. We show that such an operator does not admit a compactly supported eigenfunction, if the combinatorial curvature of the tessellation is nonpositive. Furthermore, we show that the... Read More about Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature.

Geometric heat comparison criteria for Riemannian manifolds (2006)
Journal Article
Karp, L., & Peyerimhoff, N. (2007). Geometric heat comparison criteria for Riemannian manifolds. Annals of Global Analysis and Geometry, 31, 115-145. https://doi.org/10.1007/s10455-006-9038-4

The main results of this article are small-time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions. These results are based on the geometric concepts of "(essential) distance fro... Read More about Geometric heat comparison criteria for Riemannian manifolds.

Geodesics in non-positively curved plane tessellations (2006)
Journal Article
Baues, O., & Peyerimhoff, N. (2006). Geodesics in non-positively curved plane tessellations. Advances in Geometry, 6(2), 243-263. https://doi.org/10.1515/advgeom.2006.014

We introduce a natural combinatorial curvature function on the corners of plane tessellations and relate it to the global metric geometry of their corresponding edge and dual graphs. If the combinatorial curvature in the corners is non-positive then... Read More about Geodesics in non-positively curved plane tessellations.

Spherical means on compact locally symmetric spaces of non-positive curvature (2006)
Journal Article
Peyerimhoff, N. (2006). Spherical means on compact locally symmetric spaces of non-positive curvature. Forum Mathematicum, 18(3), 391-417. https://doi.org/10.1515/forum.2006.022

We consider spherical means of continuous functions on the unit tangent bundle of a compact, non-positively curved locally symmetric space and study their behavior as the radius tends to infinity. In dimension greater or equal to 2, we prove that sph... Read More about Spherical means on compact locally symmetric spaces of non-positive curvature.