Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in euklidean spaces
We prove ϵ{epsilon}-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is δ{delta} small compared to the mean curvature. We give the explicit dependence of δ{delta} on ϵ{epsilon} within the class of uniformly convex hypersurfaces...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 April 2015
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| In: |
Bulletin of the Australian Mathematical Society
Year: 2015, Volume: 92, Issue: 1, Pages: 133-144 |
| ISSN: | 1755-1633 |
| DOI: | 10.1017/S0004972715000222 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1017/S0004972715000222 Verlag, lizenzpflichtig, Volltext: https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/quantitative-oscillation-estimates-for-almost-umbilical-closed-hypersurfaces-in-euclidean-space/A821E205EE45C9280CEEEF60306FF2F9 
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| Author Notes: | Julian Scheuer |
| Summary: | We prove ϵ{epsilon}-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is δ{delta} small compared to the mean curvature. We give the explicit dependence of δ{delta} on ϵ{epsilon} within the class of uniformly convex hypersurfaces with bounded volume. |
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| Item Description: | Gesehen am 18.06.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1755-1633 |
| DOI: | 10.1017/S0004972715000222 |