- Titel
- Geometric rigidity estimates for isometric and conformal maps from S^(n-1) to R^n
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-730906
- Datum der Einreichung
- 30.06.2020
- Datum der Verteidigung
- 11.11.2020
- Abstract (EN)
- In this thesis we study qualitative as well as quantitative stability aspects of isometric and conformal maps from S^(n-1) to R^n, when n is greater or equal to 2 or 3 respectively. Starting from the classical theorem of Liouville, according to which the isometry group of S^(n-1) is the group of its rigid motions and the conformal group of S^(n-1) is the one of its Möbius transformations, we obtain stability results for these classes of mappings among maps from S^(n-1) to R^n in terms of appropriately defined deficits. Unlike classical geometric rigidity results for maps defined on domains of R^n and mapping into R^n, not only an isometric\ conformal deficit is necessary in this more flexible setting, but also a deficit measuring how much the maps in consideration distort S^(n-1) in a generalized sense. The introduction of the latter is motivated by the classical Euclidean isoperimetric inequality.
- Freie Schlagwörter (EN)
- rigidity, stability, isoperimetric inequality
- Klassifikation (DDC)
- 500
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa2-730906
- Veröffentlichungsdatum Qucosa
- 07.12.2020
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY 4.0