A concentration Phenomenon in Mean curvature Flow.
Nobumitsu Nakauchi (1993)
Manuscripta mathematica
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Nobumitsu Nakauchi (1993)
Manuscripta mathematica
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Lohkamp, Joachim (1998)
Documenta Mathematica
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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.
Brent Collins (2001)
Visual Mathematics
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Giovanni Bellettini, Maurizio Paolini (1994)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We provide two examples of a regular curve evolving by curvature with a forcing term, which degenerates in a set having an interior part after a finite time.
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...
Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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Iyigün, Esen (2002)
APPS. Applied Sciences
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S.B. Angenent, J.J. Velázquenz (1997)
Journal für die reine und angewandte Mathematik
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Colding, Tobias H., Kleiner, Bruce (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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.
Paolini, M. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Ronaldo García, Jorge Sotomayor (2001)
Publicacions Matemàtiques
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In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [GS2], whose lines produce the extremal for the immersion, the pair of foliations by lines of...