Problèmes de Yamabe généralisés et ses applications

Yuxin Ge[1]

  • [1] Université Paris XII - Val de Marne Faculté de Sciences et Technologie Centre de Mathématiques 61 avenue du Général de Gaulle 94010 Créteil cedex (France)

Séminaire de théorie spectrale et géométrie (2006-2007)

  • Volume: 25, page 211-226
  • ISSN: 1624-5458

Abstract

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On étudie quelques équations complètement non linéaires issues de la géométrie conforme. Par une méthode de flot géométrique, on prouve l’existence des solutions. En utilisant ce résultat analytique, on obtient un théorème sur la topologie de la variété : soit M une variété riemannienne compacte de dimension 3. S’il existe une metrique g à courbure scalaire strictement positive telle que l’intégrale de la σ 2 -courbure scalaire soit positive, alors M est difféomorphe à un quotient de la sphere.

How to cite

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Ge, Yuxin. "Problèmes de Yamabe généralisés et ses applications." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 211-226. <http://eudml.org/doc/11227>.

@article{Ge2006-2007,
abstract = {On étudie quelques équations complètement non linéaires issues de la géométrie conforme. Par une méthode de flot géométrique, on prouve l’existence des solutions. En utilisant ce résultat analytique, on obtient un théorème sur la topologie de la variété : soit $M$ une variété riemannienne compacte de dimension 3. S’il existe une metrique $g$ à courbure scalaire strictement positive telle que l’intégrale de la $\sigma _2$-courbure scalaire soit positive, alors $M$ est difféomorphe à un quotient de la sphere.},
affiliation = {Université Paris XII - Val de Marne Faculté de Sciences et Technologie Centre de Mathématiques 61 avenue du Général de Gaulle 94010 Créteil cedex (France)},
author = {Ge, Yuxin},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {geometric flow; -curvature; Garding cone},
language = {fre},
pages = {211-226},
publisher = {Institut Fourier},
title = {Problèmes de Yamabe généralisés et ses applications},
url = {http://eudml.org/doc/11227},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Ge, Yuxin
TI - Problèmes de Yamabe généralisés et ses applications
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 211
EP - 226
AB - On étudie quelques équations complètement non linéaires issues de la géométrie conforme. Par une méthode de flot géométrique, on prouve l’existence des solutions. En utilisant ce résultat analytique, on obtient un théorème sur la topologie de la variété : soit $M$ une variété riemannienne compacte de dimension 3. S’il existe une metrique $g$ à courbure scalaire strictement positive telle que l’intégrale de la $\sigma _2$-courbure scalaire soit positive, alors $M$ est difféomorphe à un quotient de la sphere.
LA - fre
KW - geometric flow; -curvature; Garding cone
UR - http://eudml.org/doc/11227
ER -

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