Álvaro Martínez-Pérez
Bounded distortion homeomorphisms on ultrametric spaces.
Tue, 02/09/2010 - 16:01 — SomNambulAuthors: Álvaro Martínez-Pérez, Bruce Hughes, Manuel A. Morón
Subjects: Metric Geometry
AbstractIt is well-known that quasi-isometries between R-trees induce power
quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper
investigates power quasi-symmetric homeomorphisms between bounded, complete,
uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising
up to similarity as the end spaces of bushy trees). A bounded distortion
property is found that characterizes power quasi-symmetric homeomorphisms
between such ultrametric spaces that are also pseudo-doubling.A metric between quasi-isometric trees.
Mon, 02/08/2010 - 16:01 — SomNambulAuthors: Álvaro Martínez-Pérez
Subjects: Geometric Topology
AbstractIt is known that PQ-symmetric maps on the boundary characterize the
quasi-isometry type of visual hyperbolic spaces, in particular, of geodesically
complete \br-trees. We define a map on pairs of PQ-symmetric ultrametric spaces
which characterizes the branching of the space. We also show that, when the
ultrametric spaces are the corresponding end spaces, this map defines a metric
between rooted geodesically complete simplicial trees with minimal vertex
degree 3 in the same quasi-isometry class. Moreover, this metric measures how
far are the trees from being rooted isometric.Zig-zag chains and metric equivalences between ultrametric spaces.
Wed, 09/02/2009 - 12:02 — SomNambulAuthors: Álvaro Martínez-Pérez
Subjects: Geometric Topology
AbstractWe study the classification of ultrametric spaces based on their small scale
geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and
both (all scale uniform equivalences). We prove that these equivalences can be
characterized with parallel constructions using a combinatoric tool called
common zig-zag chain.Zig-zag chains and metric equivalences between ultrametric spaces.
Wed, 09/02/2009 - 12:02 — SomNambulAuthors: Álvaro Martínez-Pérez
Subjects: Geometric Topology
AbstractWe study the classification of ultrametric spaces based on their small scale
geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and
both (all scale uniform equivalences). We prove that these equivalences can be
characterized with parallel constructions using a combinatoric tool called
common zig-zag chain.
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