Related papers: A structure theorem for euclidean buildings

A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…

We prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space.

The ultraproduct construction is generalized to $p$-ultramean constructions ($1\leqslant p<\infty$) by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments $\mathscr L^p$ of…

We classify the epimorphisms of the buildings ${BC}_l(K,K_0,\sigma,L, q_0)$, where l is at least two, of pseudo-quadratic form type. This completes the classification of epimorphisms of irreducible spherical Moufang buildings of rank at…

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

Suppose that a metric space $X$ is the union of two metric subspaces $A$ and $B$ that embed into Euclidean space with distortions $D_A$ and $D_B$, respectively. We prove that then $X$ embeds into Euclidean space with a bounded distortion…

A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a…

We introduce the notion of ideal triangle in the Bruhat-Tits building associated to a split group -- it is analogous to the usual notion of triangle, but one vertex is "at infinity" in a certain direction. We prove that the algebraic…

We show that, for any given $q\geq 0$, any Sasakian structure on a closed manifold $M$ is approximated in the $C^{q}$-norm by structures induced by CR embeddings into weighted Sasakian spheres. In order to obtain this result, we also…

The wall-and-chamber structure is a geometric invariant that can be associated to any algebra. In this notes we give the definition of this object and we explain its relationship with torsion classes and $\tau$-tilting theory.

In this article we prove a reducibility result for the linear Schr\"odinger equation on the sphere $\mathbb{S}^{n}$ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of…

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…

We offer a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on $\mathbb{R}^n$. We use this idea to extend the result to real hyperbolic spaces $\mathbb{H}^n$.

We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the…

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation…

In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connected open Riemann surface endowed with a complete conformal Riemannian metric, if the negative part of its Gaussian curvature has finite mass,…

The goal of this work is to prove an embedding theorem for compact almost complex manifolds into complex algebraic varieties. It is shown that every almost complex structure can be realized by the transverse structure to an algebraic…

In this paper, we address the longstanding question of whether expansive homeomorphisms can exist within convex bodies in Euclidean spaces. Utilizing fundamental tools from topology, including the Borsuk-Ulam theorem and Brouwer's…

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…