Related papers: Erratum on "Hadamard spaces with isolated flats"
The main purpose of this paper is to prove the mean ergodic theorem for nonexpansive mappings and semigroups in locally compact Hadamard spaces, including finite dimensional Hadamard manifolds. The main tool for proving ergodic convergence…
S.E. Hans paper, Remarks on Pseudocovering Spaces in a Digital Topological Setting: A Corrigendum, is meant to address errors in previous papers. However, this paper is also marked by errors in its mathematics, as well as improprieties in…
We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…
We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.
The purpose of this note is to correct an inaccuracy in the paper: R.P. Agaev and P.Yu. Chebotarev, "On Determining the Eigenprojection and Components of a Matrix," Autom. Remote Control, 2002, vol. 63, pp. 1537-1545 [arXiv:math/0508197],…
Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence,…
Non-perturbative limitations on low-energy effective field theories (EFTs) based on the characteristics of high-energy theory are provided by the analyticity of the flat-space version of the S-matrix. Although the analyticity of the…
We correct an error in the article "Property (RD) for Hecke pairs".
In the paper "Uniformity of Mordell-Lang" by Vesselin Dimitrov, Philipp Habegger and Ziyang Gao (arXiv:2001.10276), they use Silverman-Tate's Height Inequality and they give a proof of the same which makes use of Cartier divisors and hence…
We show that the author of a recent paper [arXiv:2008.04929] put forward some false statements about the eigenstates of Hermitian and non-Hermitian systems. We conjecture that one of the non-Hermitian Hamiltonians for a one-dimensional…
In this paper, we present a geometric condition for a family of CAT(0) spaces, which ensures that the Izeki-Nayatani invariants of spaces in the family are uniformly bounded from above by a constant strictly less than 1. Each element of…
In this erratum we explain how to implement some axioms stated in our paper of 2009 so as to obtain a purely "local" characterization for finite $B_2$-crystals, which was declared but not clarified at some moments there. Also we correct…
This paper is a response to an article (R. de la Madrid, Journal of Physics A: Mathematical and General, 39,9255-9268 (2006)) recently published in Journal of Physics A: Mathematical and Theoretical. The article claims that the theory of…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
In this article, we give a counter-example to Lemma 12 of the article "On Operations and Linear Extensions of Well Partially Ordered Sets" by Maciej Malicki and Aleksander Rutkowski.
We present a constructive criterion for flatness of a morphism of analytic spaces X -> Y or, more generally, for flatness over Y of a coherent sheaf of modules on X. The criterion is a combination of a simple linear-algebra condition "in…
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental in performing necessary computations for, e.g., taking the…
We show that if a proper, geodesically complete, CAT(0) homology manifold is quasi-isometric to the Euclidean space R^n then it is homeomorphic to R^n. On the other hand, we show that there exist proper, geodesically complete, CAT(0) spaces…
We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm\"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of…