On uniqueness of tangent cones for Einstein manifolds

Abstract

We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.

References in corpus (3)

• Canonical Sasakian Metrics
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Monotonicity - analytic and geometric implications

Cited by in corpus (1)

• On the uniqueness of asymptotic limits of the Ricci flow