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Flats in Spaces with Convex Geodesic Bicombings

100%

Descombes D., Lang U.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes results of Bowditch for Busemann spaces.

Then-Point Condition and Rough CAT(0)

100%

Buckley S. M., Hanson B.

Analysis and Geometry in Metric Spaces

2013

tom 1

58-68

We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.

The Boundary at Infinity of a Rough CAT(0) Space

86%

Buckley S. M., Falk K.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic length space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper

Ograniczanie wyników

3 Analysis and Geometry in Metric Spaces

2 Buckley S. M.

1 Descombes D.

1 Falk K.

1 Hanson B.

1 Lang U.

1 2016

1 2014

1 2013

Wyniki wyszukiwania

Flats in Spaces with Convex Geodesic Bicombings

Then-Point Condition and Rough CAT(0)

The Boundary at Infinity of a Rough CAT(0) Space