On uniqueness of tangent cones for Einstein manifolds

By T. Colding, W. Minicozzi. 2012

105 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/28ce39f3be9f8720901619606d92d8f8647761a6

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature (2018, methodology): “ics for Du. They are achieved through a variation of the methods used in [13, Section 4]. Similar estimates have been widely considered in Colding and coauthors’ literature (see e.g. [21] [23], [22], [25]). We are providing here a complete proof. In the computations below, we are taking ﬁrst and sec”
Asymptotically conical Calabi-Yau manifolds, III (2012, background): “riety. Asymptotically conical manifolds clearly have quadratic curvature decay and Euclidean volume growth. In the Ricciat case, there are dicult regularity theorems going in the opposite direction [4, 9, 10]. However, by analysing the proof in [54], one can prove directly that the Ricciat metrics o”
Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II (2015, methodology): “In a recent work [10], using a Lojasiewicz-Simon type argument, Colding-Minicozzi proved the uniqueness under the extra assumption that there is one tangent cone with smooth cross section.”
Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, background): “ case the link of the tangent cone Y (clearly necessarily smooth, by semicontinuity of densities) is simply connected (again by volume comparison). Moreover by Cheeger-Tian [11] and Colding-Minicozzi [16]) we have Y × R is diﬀeomorphic a punctured neighborhood of the singularity, so to M × R, where ”