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Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
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Andreas Bernig
and
Alexander Lytchak
Published/Copyright:
August 1, 2007
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 equivalent. It is shown that geodesics have well-defined Euclidean directions at each point.
Received: 2004-03-03
Published Online: 2007-08-01
Published in Print: 2007-07-27
© Walter de Gruyter
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Articles in the same Issue
- Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
- Pinching estimates and motion of hypersurfaces by curvature functions
- Characters, supercharacters and Weber modular functions
- Three-dimensional Ricci solitons which project to surfaces
- Some q-analogues of the Carter-Payne theorem
- Preperiodic points of polynomials over global fields
- Orbit-counting in non-hyperbolic dynamical systems
- On intervals with few prime numbers
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