All Outputs (6)

Accurate Crystal Structures and Chemical Properties from NoSpherA2 (2020)
Journal Article
Kleemiss, F., Dolomanov, O. V., Bodensteiner, M., Peyerimhoff, N., Midgley, L., Bourhis, L. J., …Grabowsky, S. (2021). Accurate Crystal Structures and Chemical Properties from NoSpherA2. Chemical Science, 12, 1675-1692. https://doi.org/10.1039/d0sc05526c

The relationship between the structure and the properties of a drug or material is a key concept of chemistry. Knowledge of the three-dimensional structure is considered to be of such importance that almost every report of a new chemical compound is... Read More about Accurate Crystal Structures and Chemical Properties from NoSpherA2.

Curvatures, Graph Products and Ricci Flatness (2020)
Journal Article
Cushing, D., Kamtue, S., Kangaslampi, R., Liu, S., & Peyerimhoff, N. (2021). Curvatures, Graph Products and Ricci Flatness. Journal of Graph Theory, 96(4), 522-553. https://doi.org/10.1002/jgt.22630

In this paper, we compare Ollivier–Ricci curvature and Bakry–Émery curvature notions on combinatorial graphs and discuss connections to various types of Ricci flatness. We show that nonnegativity of Ollivier–Ricci curvature implies the nonnegativity... Read More about Curvatures, Graph Products and Ricci Flatness.

Signatures, Lifts, and Eigenvalues of Graphs (2020)
Book Chapter
Liu, S., Peyerimhoff, N., & Vdovina, A. (2020). Signatures, Lifts, and Eigenvalues of Graphs. In F. M. Atay, P. B. Kurasov, & D. Mugnolo (Eds.), Discrete and continuous models in the theory of networks : operator theory : advances and applications (255-269). Birkhäuser Verlag. https://doi.org/10.1007/978-3-030-44097-8_13

We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite tower of 3-cyclic lifts, each of which is again Ramanujan.

Curvature Calculations for Antitrees (2020)
Book Chapter
Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Curvature Calculations for Antitrees. In M. Keller, D. Lenz, & R. K. Wojciechowski (Eds.), Analysis and geometry on graphs and manifolds (21-54). Cambridge University Press. https://doi.org/10.1017/9781108615259.003

In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalized and non-normalized Bakry-Émery setting as well in the Ollivier-Ricci... Read More about Curvature Calculations for Antitrees.

Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature (2020)
Journal Article
Cushing, D., Kamtue, S., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in Mathematics, 360, Article 107188. https://doi.org/10.1016/j.aim.2020.107188

We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cub... Read More about Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature.

Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces (2020)
Journal Article
Knieper, G., Parker, J. R., & Peyerimhoff, N. (2020). Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces. Differential Geometry and its Applications, 69, Article 101605. https://doi.org/10.1016/j.difgeo.2020.101605

In this article we consider solvable hypersurfaces of the form with induced metrics in the symmetric space , where H a suitable unit length vector in the subgroup A of the Iwasawa decomposition . Since M is rank 2, A is 2-dimensional and we can param... Read More about Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces.