Hans-Joachim Hein

Asymptotically conical Calabi–Yau manifolds, I

This is the first part in a two-part series on complete Calabi-Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniqueness part relaxes the decay condition

Calabi-Yau manifolds with isolated conical singularities

O(r^{-n-\epsilon})

Remarks on the collapsing of torus fibered Calabi-Yau manifolds

needed in earlier work to

Weighted Sobolev inequalities under lower Ricci curvature bounds

O(r^{-\epsilon})

Asymptotically cylindrical Calabi-Yau manifolds

, relying on some new ideas about harmonic functions. We then look at a few examples: (1) Crepant resolutions of cones. This includes a new class of Ricci-flat small resolutions associated with flag manifolds. (2) Affine deformations of cones. One focus here is the question of the precise rate of decay of the metric to its tangent cone. We prove that the optimal rate for the Stenzel metric on

Gravitational instantons from rational elliptic surfaces

T^*S^n

New Logarithmic Sobolev Inequalities and an ɛ-Regularity Theorem for the Ricci Flow

is

Asymptotically conical Calabi–Yau metrics on quasi-projective varieties

-2\frac{n}{n-1}

Complete Calabi-Yau metrics from P^2 # 9 \bar P^2

.

Mass in Kähler Geometry

Let X