{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:73090"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:73090","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Geometric rigidity estimates for isometric and conformal maps from S^(n-1) to R^n","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Zemas, Konstantinos"],"institution":"Universität Leipzig","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-11-11","date_published":"2020-11-11","updated_at":"2026-07-24T03:56:21Z","subjects":["rigidity","stability","isoperimetric inequality"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Zemas, Konstantinos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Leipzig"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Leipzig"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["rigidity","stability","isoperimetric inequality"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Geometric rigidity estimates for isometric and conformal maps from S^(n-1) to R^n"]}]}],"canonical_facts":{"dc:creator":["Zemas, Konstantinos"],"dc:description.abstract":["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."],"dc:publisher":["Universitätsbibliothek Leipzig"],"dc:subject":["rigidity","stability","isoperimetric inequality"],"dc:title":["Geometric rigidity estimates for isometric and conformal maps from S^(n-1) to R^n"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Leipzig"]},"updated_at":"2026-07-24T03:56:21Z"}