Topological rigidity of compact manifolds supporting Sobolev-type inequalities

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

Preview

Text Sobolev_inequality_compact.pdf Download (411kB) | Preview

Abstract

Let (M,g) be an n-dimensional (n≥3) compact Riemannian manifold with Ric(M,g)≥(n−1)g. If (M,g) supports an AB-type 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.

Actions (login required)

Edit Item