arXiv subjects

Carlos Ramos-Cuevas

Publications and source records attributed to Carlos Ramos-Cuevas.

5 recordsLinked to original sources

arXiv2014

Subcomplexes and fixed point sets of isometries of spherical buildings

In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure of the building. We show, among other things, that if the fixed point set is top-dimensional then it is either a subbuilding or it has circumradius $\leq \fracπ{2}$. If the building is of type $A_n$ or $D_n$, we also show that the same conclusion holds for an arbitrary (top-dimensional in the $D_n$-case) convex subcomplex. This proves a conjecture of Kleiner-Leeb in these cases.

math.MG↗

arXiv2014

On the displacement function of isometries of Euclidean buildings

In this note we study the displacement function $d_g(x):=d(gx,x)$ of an isometry $g$ of a Euclidean building. We give a lower bound for $d_g(x)$ depending on the distance from $x$ to the minimal set of $g$.

math.MG↗

arXiv2013

Convexity is a local property in $CAT(κ)$ spaces

In this note we show that a connected, closed and locally convex subset (with an extra assumption on the diameter with respect to the induced length metric if $κ>0$) of a $CAT(κ)$ space is convex.

math.MG↗

arXiv2013

The generalized triangle inequalities in thick Euclidean buildings of rank 2

We describe the set of possible vector valued side lengths of n-gons in thick Euclidean buildings of rank 2. This set is determined by a finite set of homogeneous linear inequalities, which we call the generalized triangle inequalities. These inequalities are given in terms of the combinatorics of the spherical Coxeter complex associated to the Euclidean building.

math.MG↗

arXiv2013

The Center Conjecture for thick spherical buildings

In this paper we show that a convex subcomplex of a spherical building of type E6, E7 or E8 is a subbuilding or the automorphisms of the subcomplex fix a point on it. Together with previous results of Mühlherr-Tits, and Leeb and the author, this completes the proof of Tits' Center Conjecture for spherical buildings without factors of type H4, in particular, for thick spherical buildings.

math.MG↗