Real Algebraic and Analytic Geometry |

Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces.

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Submission: 2004, February 25.

*Abstract:
It is shown that the Gromov-Hausdorff limit of a subanalytic $1$-parameter
family of compact connected sets (endowed with the inner metric)
exists. If the family is semialgebraic, then the limit space can be
identified with a semialgebraic set over some real closed field.
Different notions of tangent cones (pointed Gromov-Hausdorff
limits, blow-ups and Alexandrov cones) for a closed connected
subanalytic set are studied and shown to be naturally isometric. It is
shown that geodesics have well-defined Euclidean directions at each
point.*

Mathematics Subject Classification (2000): 53C22, 32B20.

Keywords and Phrases: Tangent spaces, Gromov-Hausdorff convergence, subanalytic sets, geodesics.

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