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Geometric flows (cop. 2008) / Huai-Dong CAO
Titre : Geometric flows Type de document : texte imprimé Auteurs : Huai-Dong CAO, Editeur scientifique ; Shing-Tung YAU, Editeur scientifique Editeur : Somerville : International Press Année de publication : cop. 2008 Collection : Surveys in Differential Geometry, ISSN 1052-9233 num. XII Importance : V-347 p. ISBN/ISSN/EAN : 978-1-571-46118-6 Langues : Anglais (eng) Catégories : 53C44 Mots-clés : géométrie écoulement géométrique Note de contenu : références Geometric flows [texte imprimé] / Huai-Dong CAO, Editeur scientifique ; Shing-Tung YAU, Editeur scientifique . - International Press, cop. 2008 . - V-347 p.. - (Surveys in Differential Geometry, ISSN 1052-9233; XII) .
ISBN : 978-1-571-46118-6
Langues : Anglais (eng)
Catégories : 53C44 Mots-clés : géométrie écoulement géométrique Note de contenu : références Réservation
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Code-barres Cote Support Localisation Section Disponibilité 20987 SUR/53/8865 Livre Recherche Salle Disponible
Titre : Geometrisation of 3-manifolds Type de document : texte imprimé Auteurs : Laurent BESSIERES, Auteur ; Gérard BESSON, Auteur ; Sylvain MAILLOT, Auteur Editeur : Zürich [Suisse] : European Mathematical Society Année de publication : Cop. 2010 Collection : Tracts in mathematics num. 13 Importance : X-237 p. ISBN/ISSN/EAN : 978-3-03-719082-1 Langues : Anglais (eng) Catégories : 53C44
57-02
57M50Mots-clés : 3-variété compacte irréductible flot de Ricci à bulles conjecture de géométrisation Résumé : The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints.
Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another.
A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ?-functional and ?-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.Note de contenu : index, bibliogr. En ligne : http://www-fourier.ujf-grenoble.fr/~lbessier/english_principal.pdf Geometrisation of 3-manifolds [texte imprimé] / Laurent BESSIERES, Auteur ; Gérard BESSON, Auteur ; Sylvain MAILLOT, Auteur . - European Mathematical Society, Cop. 2010 . - X-237 p.. - (Tracts in mathematics; 13) .
ISBN : 978-3-03-719082-1
Langues : Anglais (eng)
Catégories : 53C44
57-02
57M50Mots-clés : 3-variété compacte irréductible flot de Ricci à bulles conjecture de géométrisation Résumé : The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints.
Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another.
A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ?-functional and ?-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.Note de contenu : index, bibliogr. En ligne : http://www-fourier.ujf-grenoble.fr/~lbessier/english_principal.pdf Réservation
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Code-barres Cote Support Localisation Section Disponibilité 21713 BES/57/10123 Livre Recherche Salle Disponible