dc.identifier.uri |
http://dx.doi.org/10.15488/14953 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/15072 |
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dc.contributor.author |
Smoczyk, Knut
|
|
dc.date.accessioned |
2023-10-16T07:34:26Z |
|
dc.date.available |
2023-10-16T07:34:26Z |
|
dc.date.issued |
2021 |
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dc.identifier.citation |
Smoczyk, K.: Self-Expanders of the Mean Curvature Flow. In: Vietnam Journal of Mathematics 49 (2021), Nr. 2, S. 433-445. DOI: https://doi.org/10.1007/s10013-020-00469-1 |
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dc.description.abstract |
We study self-expanding solutions Mm⊂ ℝn of the mean curvature flow. One of our main results is, that complete mean convex self-expanding hypersurfaces are products of self-expanding curves and flat subspaces, if and only if the function |A|2/|H|2 attains a local maximum, where A denotes the second fundamental form and H the mean curvature vector of M. If the principal normal ξ = H/|H| is parallel in the normal bundle, then a similar result holds in higher codimension for the function |Aξ|2/|H|2, where Aξ is the second fundamental form with respect to ξ. As a corollary we obtain that complete mean convex self-expanders attain strictly positive scalar curvature, if they are smoothly asymptotic to cones of non-negative scalar curvature. In particular, in dimension 2 any mean convex self-expander that is asymptotic to a cone must be strictly convex. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Singapore : Springer |
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dc.relation.ispartofseries |
Vietnam Journal of Mathematics 49 (2021), Nr. 2 |
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dc.rights |
CC BY 4.0 Unported |
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dc.rights.uri |
https://creativecommons.org/licenses/by/4.0 |
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dc.subject |
Mean curvature flow |
eng |
dc.subject |
Self-expander |
eng |
dc.subject.ddc |
510 | Mathematik
|
|
dc.title |
Self-Expanders of the Mean Curvature Flow |
eng |
dc.type |
Article |
|
dc.type |
Text |
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dc.relation.essn |
2305-2228 |
|
dc.relation.issn |
2305-221X |
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dc.relation.doi |
https://doi.org/10.1007/s10013-020-00469-1 |
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dc.bibliographicCitation.issue |
2 |
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dc.bibliographicCitation.volume |
49 |
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dc.bibliographicCitation.firstPage |
433 |
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dc.bibliographicCitation.lastPage |
445 |
|
dc.description.version |
publishedVersion |
eng |
tib.accessRights |
frei zug�nglich |
|