Outputs (69)

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.

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.

Random Schroedinger operators on manifolds (2003)
Journal Article
Lenz, D., Peyerimhoff, N., & Veselic, I. (2003). Random Schroedinger operators on manifolds. Markov processes and related fields, 9, 717-728

We consider a random family of Schroedinger operators on a cover of a compact Riemannian manifold. We present several results on their spectral theory, in particular almost sure constancy of th spectral components and existence and non-randomness of... Read More about Random Schroedinger operators on manifolds.

The dynamics of magnetic flows for energies above Mane's critical value (2003)
Journal Article
Peyerimhoff, N., & Siburg, K. (2003). The dynamics of magnetic flows for energies above Mane's critical value. Israel Journal of Mathematics, 135, 269-298

We show that, for energies above Mane's critical value, minimal magnetic geodesics are Riemannian (A,0)-quasi-geodesics where A -> 1 as the energy tends to infinity. As a consequence, on negatively curved manifolds, minimal magnetic geodesics lie in... Read More about The dynamics of magnetic flows for energies above Mane's critical value.

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.