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Cover: 9783034602129 | Mean Curvature Flow and Isoperimetric Inequalities | Ritoré (u. a.)
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Mean Curvature Flow and Isoperimetric Inequalities
Taschenbuch von Manuel Ritoré (u. a.)
Sprache: Englisch

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Lieferzeit 4-7 Werktage

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Beschreibung
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Inhaltsverzeichnis
Formation of Singularities in the Mean Curvature Flow.- Geometry of hypersurfaces.- Examples.- Local existence and formation of singularities.- Invariance properties.- Singular behaviour of convex surfaces.- Convexity estimates.- Rescaling near a singularity.- Huisken's monotonicity formula.- Cylindrical and gradient estimates.- Mean curvature flow with surgeries.- Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry.- The classical isoperimetric inequality in Euclidean space.- Surfaces.- Higher dimensions.- Some applications to hyperbolic geometry.
Details
Erscheinungsjahr: 2009
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 114
Inhalt: viii
114 S.
ISBN-13: 9783034602129
ISBN-10: 303460212X
Sprache: Englisch
Herstellernummer: 978-3-0346-0212-9
Autor: Ritoré, Manuel
Sinestrari, Carlo
Redaktion: Miquel, Vicente
Porti, Joan
Herausgeber: Vicente Miquel/Joan Porti
Hersteller: Birkhäuser
Springer, Basel
Birkhäuser Basel
Abbildungen: VIII, 114 p.
Von/Mit: Manuel Ritoré (u. a.)
Erscheinungsdatum: 19.10.2009
Gewicht: 0,229 kg
preigu-id: 101499170
Inhaltsverzeichnis
Formation of Singularities in the Mean Curvature Flow.- Geometry of hypersurfaces.- Examples.- Local existence and formation of singularities.- Invariance properties.- Singular behaviour of convex surfaces.- Convexity estimates.- Rescaling near a singularity.- Huisken's monotonicity formula.- Cylindrical and gradient estimates.- Mean curvature flow with surgeries.- Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry.- The classical isoperimetric inequality in Euclidean space.- Surfaces.- Higher dimensions.- Some applications to hyperbolic geometry.
Details
Erscheinungsjahr: 2009
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 114
Inhalt: viii
114 S.
ISBN-13: 9783034602129
ISBN-10: 303460212X
Sprache: Englisch
Herstellernummer: 978-3-0346-0212-9
Autor: Ritoré, Manuel
Sinestrari, Carlo
Redaktion: Miquel, Vicente
Porti, Joan
Herausgeber: Vicente Miquel/Joan Porti
Hersteller: Birkhäuser
Springer, Basel
Birkhäuser Basel
Abbildungen: VIII, 114 p.
Von/Mit: Manuel Ritoré (u. a.)
Erscheinungsdatum: 19.10.2009
Gewicht: 0,229 kg
preigu-id: 101499170
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