{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:49895"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:49895","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Chord arc submanifolds of arbitrary codimension","abstract":"In this work we extend the studies of Stephen Semmes concerning hypersurfaces which satisfy a chord-arc condition with small constant to geometric objects of higher codimension and thereby we open this subject to questions arising in the field of geometric knot theory. We consider embedded, connected, and complete submanifolds of the Euclidean space without boundary which contain the point infinity. First, we show that such submanifolds satisfy a chord-arc condition with small constant and a certain Ahlfors regularity condition, if and only if the BMO-norm of the normal spaces is small and the submanifolds satisfies a Reifenberg flatness condition with a small constant. The main tool hereby is that such submanifolds contain big portions of the graph of continuous differentiable functions. Using an extension of an approximation technique due to Semmes and a new extension theorem for isotopies, we then show that these submanifolds are diffeomorphic to spheres and are unknotted.","abstract_html":"In this work we extend the studies of Stephen Semmes concerning hypersurfaces which satisfy a chord-arc condition with small constant to geometric objects of higher codimension and thereby we open this subject to questions arising in the field of geometric knot theory. We consider embedded, connected, and complete submanifolds of the Euclidean space without boundary which contain the point infinity. First, we show that such submanifolds satisfy a chord-arc condition with small constant and a certain Ahlfors regularity condition, if and only if the BMO-norm of the normal spaces is small and the submanifolds satisfies a Reifenberg flatness condition with a small constant. The main tool hereby is that such submanifolds contain big portions of the graph of continuous differentiable functions. Using an extension of an approximation technique due to Semmes and a new extension theorem for isotopies, we then show that these submanifolds are diffeomorphic to spheres and are unknotted.","abstract_has_math":false,"creators":["Blatt, Simon"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["von der Mosel, Heiko"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-30T19:40:16Z","subjects":["info:eu-repo/classification/ddc/510","Geometrische Analysis","Differentialtopologie","Knotentheorie","Geometrische Maßtheorie","Mathematik","geometric Analysis","geometric knot theory","differential topology","geometric measure theory"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112463%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112463%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112463%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/49895","outbound_label":"Repository record","outbound_source":"dc:identifier"},"source_record":{"url":"https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A49895","prefix":"oai_dc"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["von der Mosel, Heiko"]},{"key":"dc:creator","label":"Author","values":["Blatt, Simon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2008"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22589"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/510","Geometrische Analysis","Differentialtopologie","Knotentheorie","Geometrische Maßtheorie","Mathematik","geometric Analysis","geometric knot theory","differential topology","geometric measure theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/49895","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112463%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this work we extend the studies of Stephen Semmes concerning hypersurfaces which satisfy a chord-arc condition with small constant to geometric objects of higher codimension and thereby we open this subject to questions arising in the field of geometric knot theory. We consider embedded, connected, and complete submanifolds of the Euclidean space without boundary which contain the point infinity. First, we show that such submanifolds satisfy a chord-arc condition with small constant and a certain Ahlfors regularity condition, if and only if the BMO-norm of the normal spaces is small and the submanifolds satisfies a Reifenberg flatness condition with a small constant. The main tool hereby is that such submanifolds contain big portions of the graph of continuous differentiable functions. Using an extension of an approximation technique due to Semmes and a new extension theorem for isotopies, we then show that these submanifolds are diffeomorphic to spheres and are unknotted."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University VI, 144 S. : graph. Darst. (2008). = Aachen, Techn. Hochsch., Diss., 2008"]},{"key":"dc:title","label":"Title","values":["Chord arc submanifolds of arbitrary codimension"]}]}],"canonical_facts":{"dc:contributor":["von der Mosel, Heiko"],"dc:coverage":["DE"],"dc:creator":["Blatt, Simon"],"dc:date":["2008"],"dc:description":["In this work we extend the studies of Stephen Semmes concerning hypersurfaces which satisfy a chord-arc condition with small constant to geometric objects of higher codimension and thereby we open this subject to questions arising in the field of geometric knot theory. We consider embedded, connected, and complete submanifolds of the Euclidean space without boundary which contain the point infinity. First, we show that such submanifolds satisfy a chord-arc condition with small constant and a certain Ahlfors regularity condition, if and only if the BMO-norm of the normal spaces is small and the submanifolds satisfies a Reifenberg flatness condition with a small constant. The main tool hereby is that such submanifolds contain big portions of the graph of continuous differentiable functions. Using an extension of an approximation technique due to Semmes and a new extension theorem for isotopies, we then show that these submanifolds are diffeomorphic to spheres and are unknotted."],"dc:identifier":["https://publications.rwth-aachen.de/record/49895","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112463%22"],"dc:language":["eng"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22589"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University VI, 144 S. : graph. Darst. (2008). = Aachen, Techn. Hochsch., Diss., 2008"],"dc:subject":["info:eu-repo/classification/ddc/510","Geometrische Analysis","Differentialtopologie","Knotentheorie","Geometrische Maßtheorie","Mathematik","geometric Analysis","geometric knot theory","differential topology","geometric measure theory"],"dc:title":["Chord arc submanifolds of arbitrary codimension"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:40:16Z"}