On the existence of convex hypersurfaces with prescribed mean curvature
Kaising Tso (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Kaising Tso (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Anthony Carbery, Sarah Ziesler (2002)
Publicacions Matemàtiques
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In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ 1/(n+1) introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in R2. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature. ...
E.M. Stein, C.D. Sogge (1986)
Inventiones mathematicae
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Gregory Galloway (1997)
Banach Center Publications
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Barbara Opozda, Udo Simon (2014)
Annales Polonici Mathematici
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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Patrick J. Ryan (1972)
Colloquium Mathematicae
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Hertrich-Jeromin, Udo (1994)
Beiträge zur Algebra und Geometrie
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Takehiro Itoh, Sadahiro Maeda (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
Xi-Ping Zhu (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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