Integer points close to convex hypersurfaces
M. C. Lettington (2010)
Acta Arithmetica
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M. C. Lettington (2010)
Acta Arithmetica
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Kaising Tso (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Vladimir I. Oliker (2002)
Banach Center Publications
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In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such...
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.
Patrick J. Ryan (1972)
Colloquium Mathematicae
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Kaising Tso (1992)
Mathematische Zeitschrift
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Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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F. Labourie (1987)
Inventiones mathematicae
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Toshiaki Adachi, Sadahiro Maeda (2006)
Colloquium Mathematicae
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We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
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).
J.W. Bruce (1981)
Mathematica Scandinavica
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Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Alan Weinstein, Christpher B. Croke (1981)
Inventiones mathematicae
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Andrew Baker, Nigel Ray (1982)
Mathematica Scandinavica
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Akivis, Maks A., Goldberg, Vladislav V. (1998)
Beiträge zur Algebra und Geometrie
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Th. Koufogiorgos, C. Baikoussis (1988)
Monatshefte für Mathematik
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