Degenerate neckpinches in mean curvature flow.
S.B. Angenent, J.J. Velázquenz (1997)
Journal für die reine und angewandte Mathematik
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S.B. Angenent, J.J. Velázquenz (1997)
Journal für die reine und angewandte Mathematik
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Norbert Jakobowsky (1994)
Journal für die reine und angewandte Mathematik
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U. Abresch (1987)
Journal für die reine und angewandte Mathematik
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Viktor Schroeder (1988)
Journal für die reine und angewandte Mathematik
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Mayer, Uwe F. (2001)
Experimental Mathematics
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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.
Klaus Deckelnick (1995)
Journal für die reine und angewandte Mathematik
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Nobumitsu Nakauchi (1993)
Manuscripta mathematica
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Colding, Tobias H., Kleiner, Bruce (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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Y.L. Xin, Rugang Ye (1997)
Journal für die reine und angewandte Mathematik
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Xu-Jia Wang (2014)
Journal of the European Mathematical Society
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The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
Lohkamp, Joachim (1998)
Documenta Mathematica
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Simon Newcomb (1877)
Journal für die reine und angewandte Mathematik
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Brent Collins (2001)
Visual Mathematics
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Esther Cabezas-Rivas, Burkhard Wilking (2015)
Journal of the European Mathematical Society
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We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open...