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Sectional curvature of polygonal complexes with planar substructures

Keller, Matthias; Peyerimhoff, Norbert; Pogorzelski, Felix

Sectional curvature of polygonal complexes with planar substructures Thumbnail


Matthias Keller

Felix Pogorzelski


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 of non-positive and negative combinatorial curvature. As geometric results we obtain a Hadamard–Cartan type theorem, thinness of bigons, Gromov hyperbolicity and estimates for the Cheeger constant. We employ the latter to get spectral estimates, show discreteness of the spectrum in the sense of a Donnelly–Li type theorem and present corresponding eigenvalue asymptotics. Moreover, we prove a unique continuation theorem for eigenfunctions and the solvability of the Dirichlet problem at infinity.


Keller, M., Peyerimhoff, N., & Pogorzelski, F. (2017). Sectional curvature of polygonal complexes with planar substructures. Advances in Mathematics, 307, 1070-1107.

Journal Article Type Article
Acceptance Date Oct 24, 2016
Online Publication Date Dec 6, 2016
Publication Date Feb 5, 2017
Deposit Date Oct 24, 2016
Publicly Available Date Oct 25, 2016
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 307
Pages 1070-1107


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