Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
Type of Publication: | Journal article |
Publication status: | Published |
Author: | Schulze, Felix; Schnürer, Oliver C. |
Year of publication: | 2006 |
Published in: | Annali della Scuola Normale Superiore di Pisa : Classe di Scienze ; 5 (2006), 5. - pp. 273-277. - ISSN 0036-9918 |
URL of original publication: | http://www.numdam.org/item/ASNSP_2006_5_5_2_261_0, Last access on Jan 12, 2018 |
Summary: |
We study the evolution of a closed, convex hypersurface in Rn+1 in direction of its normal vector, where the speed equals a power k≥1 of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to 1, depending only on k and n, then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.
|
Subject (DDC): | 510 Mathematics |
Files | Size | Format | View |
---|---|---|---|
There are no files associated with this item. |
SCHULZE, Felix, Oliver C. SCHNÜRER, 2006. Appendix to: Convexity estimates for flows by powers of the mean curvature. In: Annali della Scuola Normale Superiore di Pisa : Classe di Scienze. 5(5), pp. 273-277. ISSN 0036-9918
@article{Schulze2006Appen-41191, title={Appendix to: Convexity estimates for flows by powers of the mean curvature}, url={http://www.numdam.org/item/ASNSP_2006_5_5_2_261_0}, year={2006}, number={5}, volume={5}, issn={0036-9918}, journal={Annali della Scuola Normale Superiore di Pisa : Classe di Scienze}, pages={273--277}, author={Schulze, Felix and Schnürer, Oliver C.} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/41191"> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:creator>Schnürer, Oliver C.</dc:creator> <dc:contributor>Schnürer, Oliver C.</dc:contributor> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:creator>Schulze, Felix</dc:creator> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/41191"/> <dc:language>eng</dc:language> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-01T15:16:13Z</dc:date> <dcterms:issued>2006</dcterms:issued> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-01T15:16:13Z</dcterms:available> <dcterms:abstract xml:lang="eng">We study the evolution of a closed, convex hypersurface in Rn+1 in direction of its normal vector, where the speed equals a power k≥1 of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to 1, depending only on k and n, then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.</dcterms:abstract> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:title>Appendix to: Convexity estimates for flows by powers of the mean curvature</dcterms:title> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Schulze, Felix</dc:contributor> </rdf:Description> </rdf:RDF>