Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
- Bernig, Andreas Département de Mathématiques, Université de Fribourg, Switzerland
- Lytchak, Alexander Mathematisches Institut, Universität Bonn, Germany
-
2007
Published in:
- Journal für die reine und angewandte Mathematik. - 2007, no. 608, p. 1-15
English
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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 8430
- DOI 10.1515/CRELLE.2007.050
- Persistent URL
- https://folia.unifr.ch/unifr/documents/300417
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