Starshaped hypersurfaces and the mean curvature flow.
Knut Smoczyk (1998)
Manuscripta mathematica
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Knut Smoczyk (1998)
Manuscripta mathematica
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Klaus Ecker, Gerhard Huisken (1991)
Inventiones mathematicae
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Giuseppe Pipoli (2017)
Complex Manifolds
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In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.
Gerhard Huisken (1987)
Mathematische Zeitschrift
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Rolf Schneider (1983)
Annales Polonici Mathematici
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Kaising Tso (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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B. Chow (1987)
Inventiones mathematicae
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Klaus Ecker, Gerhard Huisken (1989)
Mathematische Annalen
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Rolf Walter (1985)
Mathematische Annalen
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Huisken, Gerhard (1998)
Documenta Mathematica
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Julian Scheuer (2015)
Geometric Flows
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We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial...