On the Existence of Integral Currents with Prescribed Mean Curvature Vector.
Martin Fuchs, Frank Duzaar (1990)
Manuscripta mathematica
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Martin Fuchs, Frank Duzaar (1990)
Manuscripta mathematica
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Liang-Khoon Koh (1997)
Manuscripta mathematica
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Mayer, Uwe F. (2001)
Experimental Mathematics
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Ulrich Dierkes (1986)
Manuscripta mathematica
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Neil S. Trudinger (1990)
Manuscripta mathematica
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Rolf Walter (1989)
Manuscripta 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.
Lohkamp, Joachim (1998)
Documenta Mathematica
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Michael T. Anderson (1990)
Manuscripta mathematica
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Brent Collins (2001)
Visual Mathematics
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Robert Gulliver (1973/74)
Manuscripta mathematica
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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...
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.