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The local structure of length spaces with curvature bounded above
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In this article, it was shown that if X is a locally compact CAT(0) space with cocompact isometry group, then the dimension of the Tits boundary and the asymptotic cone(s) of X are determined by the maximal dimension of a flat in X.Abstract:
We show that a number of different notions of dimension coincide for length spaces with curvature bounded above. We then apply this result, showing that if X is a locally compact CAT(0) space with cocompact isometry group, then the dimension of the Tits boundary and the asymptotic cone(s) of X are determined by the maximal dimension of a flat in X.read more
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Book
A Course in Metric Geometry
TL;DR: In this article, a large-scale Geometry Spaces of Curvature Bounded Above Spaces of Bounded Curvatures Bounded Below Bibliography Index is presented. But it is based on the Riemannian metric space.
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Currents in metric spaces
Luigi Ambrosio,Bernd Kirchheim +1 more
TL;DR: In this article, the authors consider the generalized plateau problem and show that the solution of the generalized plateau problem is equivalent to the closure and boundary-rectifiability theorems for Euclidean currents.
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Lectures on Lipschitz analysis
TL;DR: The theory of Lipschitz functions in Euclidean spaces was studied in this paper, where it was shown that a function is a Lipschnitz function if it is L-Lipschnitzer for some L.
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Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups
TL;DR: In the context of cubical cubical groups, the authors showed that the quasi-Lipschitz image from a ball in a nilpotent Lie group into a hierarchically hyperbolic space lies close to a product of hierarchy geodesics.
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Simplical volume of closed locally symmetric spaces of non-compact type
TL;DR: In this paper, it was shown that locally symmetric spaces of non-compact type have positive simplicial volume, a question first raised by Gromov in Inst Hautes Etudes Sci Publ Math 56:5, 1982.
References
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Buildings of Spherical Type and Finite BN-Pairs
TL;DR: In this article, the building of a semi-simple algebraic group is defined as the construction of a building of type An, Dn, En., Buildings of type Cn. I. Polar spaces.
Book
Strong Rigidity of Locally Symmetric Spaces.
TL;DR: In this paper, a metric definition of the Maximal Boundary is defined and a map of R-Rank 1 is presented. But this map does not cover all R-rank 1 spaces.
Book
Manifolds of Nonpositive Curvature
TL;DR: In this paper, the authors presented a lecture on simply connected manifolds of non-positive curvature and groups of isometries, and showed that strong rigidity of locally symmetric spaces can be achieved for non-analytic menifolds.