On établit la compacité des solutions du problème de Yamabe sur toute variété riemannienne, régulière compacte connexe (non conformément équivalente à la sphère standard) de dimension n⩽7. Le même résultat est valable en dimension n⩾8 sous une hypothèse supplémentaire.
We establish compactness of solutions to the Yamabe problem on any smooth compact connected Riemannian manifold (not conformally diffeomorphic to standard spheres) of dimension n⩽7 as well as on any manifold of dimension n⩾8 under some additional hypothesis.
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@article{CRMATH_2004__338_9_693_0, author = {Li, YanYan and Zhang, Lei}, title = {Compactness of solutions to the {Yamabe} problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {693--695}, publisher = {Elsevier}, volume = {338}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.02.018}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2004.02.018/} }
TY - JOUR AU - Li, YanYan AU - Zhang, Lei TI - Compactness of solutions to the Yamabe problem JO - Comptes Rendus. Mathématique PY - 2004 SP - 693 EP - 695 VL - 338 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.02.018/ DO - 10.1016/j.crma.2004.02.018 LA - en ID - CRMATH_2004__338_9_693_0 ER -
Li, YanYan; Zhang, Lei. Compactness of solutions to the Yamabe problem. Comptes Rendus. Mathématique, Tome 338 (2004) no. 9, pp. 693-695. doi : 10.1016/j.crma.2004.02.018. http://www.numdam.org/articles/10.1016/j.crma.2004.02.018/
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