Evolution of hypersurfaces by their curvature in Riemannian manifolds.
Huisken, Gerhard (1998)
Documenta Mathematica
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Huisken, Gerhard (1998)
Documenta Mathematica
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El-Tawil, Magdy A., El-Hazmy, Maha A. (2009)
Differential Equations & Nonlinear Mechanics
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Sarti, A., Citti, G. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Thomas Richard (2012-2014)
Séminaire de théorie spectrale et géométrie
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This survey reviews some facts about nonnegativity conditions on the curvature tensor of a Riemannian manifold which are preserved by the action of the Ricci flow. The text focuses on two main points. First we describe the known examples of preserved curvature conditions and how they have been used to derive geometric results, in particular sphere theorems. We then describe some recent results which give restrictions on general preserved conditions. ...
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.
Paolini, M. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Yonathan Aflalo, Anastasia Dubrovina, Ron Kimmel, Aaron Wetzler (2013)
Actes des rencontres du CIRM
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The laplacian operator applied to the coordinates of a manifold provides the mean curvature vector. Manipulating the metric of the manifold or interpreting its coordinates in various ways provide useful tools for shape and image processing and representation. We will review some of these tools focusing on scale invariant geometry, curvature flow with respect to an embedding of the image manifold in a high dimensional space, and object segmentation by active contours defined via the shape...
Schmidt, A. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Sarić, Branko (2000)
Lobachevskii Journal of Mathematics
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Weickert, J. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Wolfgang Tutschke (1985)
Annales Polonici Mathematici
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Azmy S. Ackleh, Robert R. Ferdinand, Simeon Reich (1998)
Kybernetika
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We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.