Related papers: A structure theorem for euclidean buildings

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and…

The Urysohn space is a complete separable metric space, universal among separable metric spaces for extending finite partial isometries into it. We present an alternative construction of the Urysohn space which enables us to show that…

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the…

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

A classical theorem states that two confocal ellipsoids, each of them endowed with a surface distribution of mass which is called homeoidal, exert the same Newtonian force on an exterior point if they have the same total mass. We extend…

We prove that a Poisson boundary of any regular thick Euclidean building, as well as lattices thereof is the space of chambers at infinity of the building with the harmonic measure class. We then use this result to generalize rigidity…

We show that any equivalence of bounded derived categories of coherent sheaves on a smooth projective complex variety supported in a closed algebraic subset preserves the dimension of the support in two cases: (i) the restriction of the…

We show that there exists a quasi-isometric embedding of the product of $n$ copies of $\mathbb{H}_{\mathbb{R}}^2$ into any symmetric space of non-compact type of rank $n$, and there exists a bi-Lipschitz embedding of the product of $n$…

The following is an open problem in topology: Determine whether the Stone-\v{C}ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

In this paper, we present a converse to a version of Skoda's $L^2$ division theorem by investigating the solvability of $\bar{\partial}$ equations of a specific type.

In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.

The Erd\H{o}s-Anning theorem states that every point set in the Euclidean plane with integer distances must be either collinear or finite. More strongly, for any (non-degenerate) triangle of diameter~$\delta$, at most $O(\delta^2)$ points…

The main result of this article is a geometric interpretation of magnitude, a real-valued invariant of metric spaces. We introduce a Euclidean embedding of a (suitable) finite metric space $X$ such that the magnitude of $X$ can be expressed…

We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings…

We prove that for a chainable continuum $X$ and every non-zigzag $x\in X$ there exists a planar embedding $\phi:X\to \phi(X)\subset\mathbb R^2$ such that $\phi(x)$ is accessible, partially answering the question of Nadler and Quinn from…

A finite set X in the Euclidean space is called an s-inner product set if the set of the usual inner products of any two distinct points in X has size s. First, we give a special upper bound for the cardinality of an s-inner product set on…

In the Euclidean setting, Napoleon's Theorem states that if one constructs an equilateral triangle on either the outside or the inside of each side of a given triangle and then connects the barycenters of those three new triangles, the…