A remark on almost umbilical hypersurfaces
Archivum Mathematicum (2013)
- Volume: 049, Issue: 1, page 1-7
- ISSN: 0044-8753
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topRoth, Julien. "A remark on almost umbilical hypersurfaces." Archivum Mathematicum 049.1 (2013): 1-7. <http://eudml.org/doc/252494>.
@article{Roth2013,
abstract = {In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.},
author = {Roth, Julien},
journal = {Archivum Mathematicum},
keywords = {hypersurfaces; rigidity; pinching; Ricci curvature; umbilicity tensor; higher order mean curvatures; $\theta $-quasi-isometry; hypersurfaces; rigidity; pinching; Ricci curvature; umbilicity tensor; higher-order mean curvatures; -quasi-isometry},
language = {eng},
number = {1},
pages = {1-7},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A remark on almost umbilical hypersurfaces},
url = {http://eudml.org/doc/252494},
volume = {049},
year = {2013},
}
TY - JOUR
AU - Roth, Julien
TI - A remark on almost umbilical hypersurfaces
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 1
SP - 1
EP - 7
AB - In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
LA - eng
KW - hypersurfaces; rigidity; pinching; Ricci curvature; umbilicity tensor; higher order mean curvatures; $\theta $-quasi-isometry; hypersurfaces; rigidity; pinching; Ricci curvature; umbilicity tensor; higher-order mean curvatures; -quasi-isometry
UR - http://eudml.org/doc/252494
ER -
References
top- Aubry, E., Finiteness of and geometric inequalities in almost positive Ricci curvature, Ann. Sci. École Norm. Sup. (4) 40 (4) (2007), 6757–695. (2007) Zbl1141.53034MR2191529
- Colbois, B., Grosjean, J. F., 10.4171/CMH/88, Comment. Math. Helv. 82 (2007), 175–195. (2007) Zbl1112.53003MR2296061DOI10.4171/CMH/88
- Fialkow, A., 10.2307/1968462, Ann. of Math. (2) 39 (1938), 762–783. (1938) Zbl0020.06601MR1503435DOI10.2307/1968462
- Grosjean, J. F., 10.2140/pjm.2002.206.93, Pacific J. Math. 206 (1) (2002), 93–111. (2002) MR1924820DOI10.2140/pjm.2002.206.93
- Grosjean, J. F., Roth, J., 10.1007/s00209-011-0872-0, Math. Z. 271 (1) (2012), 469–488. (2012) Zbl1243.53071MR2917153DOI10.1007/s00209-011-0872-0
- Hoffman, D., Spruck, D., 10.1002/cpa.3160270601, Comm. Pure Appl. Math. 27 (1974), 715–727. (1974) Zbl0295.53025MR0365424DOI10.1002/cpa.3160270601
- Reilly, R.C., 10.1007/BF02567385, Comment. Math. Helv. 52 (1977), 525–533. (1977) Zbl0382.53038MR0482597DOI10.1007/BF02567385
- Roth, J., 10.1007/s10455-007-9086-4, Ann. Global Anal. Geom. 33 (3) (2008), 293–306. (2008) MR2390836DOI10.1007/s10455-007-9086-4
- Shiohama, K., Xu, H., 10.2206/kyushujm.48.291, Kyushu J. Math. 48 (2) (1994), 291–306. (1994) Zbl0826.53045MR1294532DOI10.2206/kyushujm.48.291
- Shiohama, K., Xu, H., 10.2206/kyushujm.54.103, Kyushu J. Math. 54 (1) (2000), 103–109. (2000) Zbl1005.53028MR1762795DOI10.2206/kyushujm.54.103
- Thomas, T. Y., 10.2307/2371240, Amer. J. Math. 58 (1936), 702–704. (1936) MR1507192DOI10.2307/2371240
- Vlachos, T., Almost-Einstein hypersurfaces in the Euclidean space, Illinois J. Math. 53 (4) (2009), 1221–1235. (2009) Zbl1213.53072MR2741186
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