Farkas, Csaba and Kristály, Alexandru and Mester, Ágnes (2018) Topological rigidity of compact manifolds supporting Sobolevtype inequalities. (Submitted)

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Abstract
Let (M,g) be an ndimensional (n≥3) compact Riemannian manifold with Ric(M,g)≥(n−1)g. If (M,g) supports an ABtype critical Sobolev inequality with Sobolev constants close to the optimal ones corresponding to the standard unit sphere (Sn,g0), we prove that (M,g) is topologically close to (Sn,g0). Moreover, the Sobolev constants on (M,g) are precisely the optimal constants on the sphere (Sn,g0) if and only if (M,g) is isometric to (Sn,g0); in particular, the latter result answers a question of V.H. Nguyen.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis 
Depositing User:  Dr. Alexandru Kristaly 
Date Deposited:  25 Sep 2019 14:32 
Last Modified:  25 Sep 2019 14:32 
URI:  http://real.mtak.hu/id/eprint/101253 
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