H. Hein

activity

20102022

most citedAsymptotically conical Calabi-Yau manifolds, I

75 citations · 199 across the 15 of their papers we have counts for

collaborators

18 papers

math.DG2022★ 1 cited

Classification of asymptotically conical Calabi-Yau manifolds

Ronan J. Conlon, Hans-Joachim Hein

A Riemannian cone $(C, g_{C})$ is by definition a warped product $C = R^{+} \times L$ with metric $g_{C} = d r^{2} \oplus r^{2} g_{L}$ , where $(L, g_{L})$ is a compact Riemannian manifold…

math.DG2021

Asymptotically Calabi metrics and weak Fano manifolds

Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1

We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises f…

math.DG2021

Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps

Xin Fu, Hans-Joachim Hein, Xumin Jiang

Let $L$ be a negative holomorphic line bundle over an $(n - 1)$ -dimensional complex torus $D$ . Let $h$ be a Hermitian metric on $L$ such that the curvature form of the dual Hermitian…

math.DG2021★ 5 cited

Smooth asymptotics for collapsing Calabi-Yau metrics

Hans-Joachim Hein, Valentino Tosatti

We prove that Calabi-Yau metrics on compact Calabi-Yau manifolds whose Kahler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from t…

math.DG2019

The renormalized volume of a 4-dimensional Ricci-flat ALE space

Olivier Biquard, Hans-Joachim Hein

We introduce a natural definition of the renormalized volume of a 4-dimensional Ricci-flat ALE space. We then prove that the renormalized volume is always less or equal than zero,…

math.DG2018★ 24 cited

Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces

Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1

We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding con…

math.DG2018★ 22 cited

Higher-order estimates for collapsing Calabi-Yau metrics

Hans-Joachim Hein, Valentino Tosatti

We prove a uniform C^alpha estimate for collapsing Calabi-Yau metrics on the total space of a proper holomorphic submersion over the unit ball in C^m. The usual methods of Calabi,…

math.DG2017

A Liouville theorem for the complex Monge-Ampère equation on product manifolds

Hans-Joachim Hein

Let $Y$ be a closed Calabi-Yau manifold. Let $ω$ be the Kähler form of a Ricci-flat Kähler metric on $C^{m} \times Y$ . We prove that if $ω$ is uniformly bounded above and be…

math.DG2016

On the classification of ALE Kähler manifolds

Hans-Joachim Hein, Rares Rasdeaconu, Ioana Suvaina

The underlying complex structure of an ALE Kähler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only fin…

math.DG2016★ 12 cited

Calabi-Yau manifolds with isolated conical singularities

Hans-Joachim Hein, Song Sun

Let $X$ be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let $L$ be an ample line bundle on $X$ . Assume that the pair $(X, L)$ is…

math.DG2015

Mass in Kähler Geometry

Hans-Joachim Hein, Claude LeBrun

We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kähler manifold, assuming only the sort of weak fall-off conditions required for the…

math.DG2014★ 1 cited

Asymptotically conical Calabi-Yau manifolds, III

Ronan J. Conlon, Hans-Joachim Hein

In a recent preprint, Chi Li proved that aymptotically conical complex manifolds with regular tangent cone at infinity admit holomorphic compactifications (his result easily extend…

math.DG2014★ 43 cited

Remarks on the collapsing of torus fibered Calabi-Yau manifolds

Hans-Joachim Hein, Valentino Tosatti

One of the main results of the paper arXiv:1108.0967 by Gross-Tosatti-Zhang establishes estimates on the collapsing of Ricci-flat Kahler metrics on holomorphic torus fibrations. We…

math.DG2013★ 4 cited

Asymptotically conical Calabi-Yau metrics on quasi-projective varieties

Ronan J. Conlon, Hans-Joachim Hein

Let X be a compact Kahler orbifold without \C-codimension-1 singularities. Let D be a suborbifold divisor in X such that D \supset Sing(X) and -pK_X = q[D] for some p, q \in \N wit…

math.DG2012★ 7 cited

Asymptotically cylindrical Calabi-Yau manifolds

Mark Haskins, Hans-Joachim Hein, Johannes Nordström

Let $M$ be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to $[0, \infty) \times X$ for some compact connected Ricci-fl…

math.DG2012

New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow

Hans-Joachim Hein, Aaron Naber

In this note we prove a new ε-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) i…

math.DG2012★ 75 cited

Asymptotically conical Calabi-Yau manifolds, I

Ronan J. Conlon, Hans-Joachim Hein

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 result…

math.DG2010★ 5 cited

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

Hans-Joachim Hein

Let $X$ denote the complex projective plane, blown up at the nine base points of a pencil of cubics, and let $D$ be any fiber of the resulting elliptic fibration on $X$ . Using ansa…