Pincement sur le spectre et le volume en courbure de Ricci positive

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• 作者：Erwann Aubry
• 刊名：Annales Scientifiques de l'Ecole Normale Superieure
• 出版年：2005
• 期刊代码：1_00129593
• 类别：mt
• 出版时间：2005
• 卷：38
• 期：3
• 页码：387-405
• 文件大小：238 K

摘要

We shall show that a complete Riemannian manifold of dimension n with decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKH-4H2F7JV-3&_mathId=mml7&_user=10&_cdi=6123&_rdoc=3&_handle=V-WA-A-W-Z-MsSAYVA-UUW-U-AABZBUDEZV-AABBYYYDZV-CADDBDZZY-Z-U&_acct=C000050221&_version=1&_userid=10&md5=8ead417dc418ae702c1c9de470b494c5" title="Click to view the MathML source">Ricder=0>n−1 and its n-st eigenvalue close to n is both Gromov–Hausdorff close and diffeomorphic to the standard sphere. This extends, in an optimal way, a result of P. Petersen [Invent. Math. 138 (1999) 1] (as a by-product, we fill a gap stated in the erratum [Invent. Math. 155 (2004) 223]). We shall also show that a manifold with decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKH-4H2F7JV-3&_mathId=mml8&_user=10&_cdi=6123&_rdoc=3&_handle=V-WA-A-W-Z-MsSAYVA-UUW-U-AABZBUDEZV-AABBYYYDZV-CADDBDZZY-Z-U&_acct=C000050221&_version=1&_userid=10&md5=f72bd94ca79e9520e9d7bee192b895f4" title="Click to view the MathML source">Ricder=0>n−1 and volume close to der="0" height=24 width=50> is both Gromov–Hausdorff close and diffeomorphic to a space form der="0" height=16 width=72>. This extends results of T. Colding [Invent. Math. 124 (1996) 175] and T. Yamaguchi [Math. Ann. 284 (1989) 423].