Outputs (69)

Eigenvalue ratios of non-negatively curved graphs (2018)
Journal Article
Liu, S., & Peyerimhoff, N. (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, Probability and Computing, 27(5), 829-850. https://doi.org/10.1017/s0963548318000214

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality CD(0, ∞). This estimate is independent of the size of the graph and provides a general method to obtain higher-order spectral esti... Read More about Eigenvalue ratios of non-negatively curved graphs.

Bakry–Émery curvature and diameter bounds on graphs (2018)
Journal Article
Liu, S., Münch, F., & Peyerimhoff, N. (2018). Bakry–Émery curvature and diameter bounds on graphs. Calculus of Variations and Partial Differential Equations, 57(2), Article 67. https://doi.org/10.1007/s00526-018-1334-x

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an a... Read More about Bakry–Émery curvature and diameter bounds on graphs.

Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space (2017)
Journal Article
Peyerimhoff, N., Täufer, M., & Veselić, I. (2017). Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space. Nanosistemy: fizika, himiâ, matematika Наносистемы: физика, химия, математика (Print), 8(2), 216-230. https://doi.org/10.17586/2220-8054-2017-8-2-216-230

For the analysis of the Schrödinger and related equations it is of central importance whether a unique continuation principle (UCP) holds or not. In continuum Euclidean space, quantitative forms of unique continuation imply Wegner estimates and regul... Read More about Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space.

Sectional curvature of polygonal complexes with planar substructures (2016)
Journal Article
Keller, M., Peyerimhoff, N., & Pogorzelski, F. (2017). Sectional curvature of polygonal complexes with planar substructures. Advances in Mathematics, 307, 1070-1107. https://doi.org/10.1016/j.aim.2016.10.027

In this paper we introduce a class of polygonal complexes for which we consider a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus on the case... Read More about Sectional curvature of polygonal complexes with planar substructures.

Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians (2015)
Journal Article
Lange, C., Liu, S., Peyerimhoff, N., & Post, O. (2015). Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians. Calculus of Variations and Partial Differential Equations, 54(4), 4165-4196. https://doi.org/10.1007/s00526-015-0935-x

We discuss a Cheeger constant as a mixture of the frustration index and the expansion rate, and prove the related Cheeger inequalities and higher order Cheeger inequalities for graph Laplacians with cyclic signatures, discrete magnetic Laplacians on... Read More about Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians.

Geometric properties of rank one asymptotically harmonic manifolds (2015)
Journal Article
Knieper, G., & Peyerimhoff, N. (2015). Geometric properties of rank one asymptotically harmonic manifolds. Journal of Differential Geometry, 100(3), 507-532. https://doi.org/10.4310/jdg/1432842363

In this article we consider asymptotically harmonic manifolds which are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature h. We prove the following equivalences for... Read More about Geometric properties of rank one asymptotically harmonic manifolds.

Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials (2015)
Journal Article
Leonhardt, K., Peyerimhoff, N., Tautenhahn, M., & Veselic, I. (2015). Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials. Reviews in Mathematical Physics, 27(04), https://doi.org/10.1142/s0129055x15500075

We study Schrödinger operators on L2(ℝd) and ℓ2(ℤd) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting, we require a generalized step-fu... Read More about Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials.

Harmonic Functions on Rank One Asymptotically Harmonic Manifolds (2015)
Journal Article
Knieper, G., & Peyerimhoff, N. (2015). Harmonic Functions on Rank One Asymptotically Harmonic Manifolds. Journal of Geometric Analysis, 26(2), 750-781. https://doi.org/10.1007/s12220-015-9570-1

Asymptotically harmonic manifolds are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature hh. In this article we present results for harmonic functions on rank one as... Read More about Harmonic Functions on Rank One Asymptotically Harmonic Manifolds.

An infinite family of 2-groups with mixed Beauville structures (2014)
Journal Article
Barker, N., Boston, N., Peyerimhoff, N., & Vdovina, A. (2015). An infinite family of 2-groups with mixed Beauville structures. International Mathematics Research Notices, 2015(11), 3598-3618. https://doi.org/10.1093/imrn/rnu045

We construct an infinite family of triples (Gk, Hk, Tk), where Gk are 2-groups of increasing order, Hk are index 2 subgroups of Gk, and Tk are pairs of generators of Hk. We show that the triples uk = (Gk, Hk, Tk) are mixed Beauville structures if k i... Read More about An infinite family of 2-groups with mixed Beauville structures.

Integral Geometric Properties of Non-compact Harmonic Spaces (2013)
Journal Article
Peyerimhoff, N., & Samiou, E. (2015). Integral Geometric Properties of Non-compact Harmonic Spaces. Journal of Geometric Analysis, 25(1), Article 122. https://doi.org/10.1007/s12220-013-9416-7

On non-compact harmonic manifolds we prove that functions satisfying the mean value property for two generic radii must be harmonic. Moreover, functions with vanishing integrals over all spheres (or balls) of two generic radii must be identically zer... Read More about Integral Geometric Properties of Non-compact Harmonic Spaces.