75 citations · 135 across the 20 of their papers we have counts for
24 papers
Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton
Ronan J. Conlon, Alix Deruelle
We establish the uniqueness of the soliton vector field of a complete shrinking gradient Kähler-Ricci soliton up to pushforward by biholomorphism.
Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Charles Cifarelli, Ronan Conlon, Max Hallgren +1
For any volume-collapsing finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface, we show the flow satisfies a Type I curvature bound and classify the correspon…
Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones
Ronan J. Conlon, Alix Deruelle
We show that any complete shrinking gradient Kähler-Ricci soliton on a resolution of a Kähler cone is necessarily asymptotically conical. From a result of Esparza, it then follows…
New examples of affine Calabi-Yau 3-folds with maximal volume growth
Shih-Kai Chiu, Ronan J. Conlon, Frédéric Rochon
We construct examples of complete Calabi-Yau metrics on smoothings of 3-dimensional Calabi-Yau cones that are not products of lower-dimensional Calabi-Yau cones and that have orbif…
A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity
Richard H. Bamler, Eric Chen, Ronan J. Conlon
We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Kähler…
An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for
Ivin Babu, Ronan J. Conlon, Alix Deruelle
We show that any toric asymptotically conical shrinking gradient Kähler-Ricci soliton on an anti-canonically polarised resolution of a Kähler cone satisfies a complex Monge-Ampère…
Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
Ronan J. Conlon, Tran-Trung Nghiem
We present infinitely many new examples of affine Calabi--Yau manifolds of Euclidean volume growth and quadratic curvature decay, whose tangent cones at infinity are irregular and…
Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Ronan J. Conlon, Max Hallgren, Zilu Ma
We show that any non-collapsed finite time singularity of the Ricci flow on a compact Kähler surface is of Type I. Combined with a previous result of the first author, Cifarelli, a…
A family of Kähler flying wing steady Ricci solitons
Pak-Yeung Chan, Ronan J. Conlon, Yi Lai
In , H.-D. Cao constructed a -invariant steady gradient Kähler-Ricci soliton on and asked whether every steady gradient Kähler-Ricci soliton of positiv…
Warped quasi-asymptotically conical Calabi-Yau metrics
Ronan J. Conlon, Frédéric Rochon
We construct many new examples of complete Calabi-Yau metrics of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones with smooth cross-sections. A…
A new complete two-dimensional shrinking gradient Kähler-Ricci soliton
Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon +1
We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of at one point. Th…
An Aubin continuity path for shrinking gradient Kähler-Ricci solitons
Charles Cifarelli, Ronan J. Conlon, Alix Deruelle
Let be a toric Kähler-Einstein Fano manifold. We show that any toric shrinking gradient Kähler-Ricci soliton on certain toric blowups of satisfies a comple…
On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces
Charles Cifarelli, Ronan J. Conlon, Alix Deruelle
We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient Kähler-Ricci soliton with soliton metric with…
Classification of asymptotically conical Calabi-Yau manifolds
Ronan J. Conlon, Hans-Joachim Hein
A Riemannian cone is by definition a warped product with metric , where is a compact Riemannian manifold…
Steady gradient Kähler-Ricci solitons on crepant resolutions of Calabi-Yau cones
Ronan J. Conlon, Alix Deruelle
We show that, up to the flow of the soliton vector field, there exists a unique complete steady gradient Kähler-Ricci soliton in every Kähler class of an equivariant crepant resolu…
Classification results for expanding and shrinking gradient Kähler-Ricci solitons
Ronan J. Conlon, Alix Deruelle, Song Sun
We first show that a Kähler cone appears as the tangent cone of a complete expanding gradient Kähler-Ricci soliton with quadratic curvature decay with derivatives if and only if it…
New examples of complete Calabi-Yau metrics on for
Ronan J. Conlon, Frédéric Rochon
For each , we construct on examples of complete Calabi-Yau metrics of Euclidean volume growth having a tangent cone at infinity with singular cross-section.
Quasi-asymptotically conical Calabi-Yau manifolds
Ronan J. Conlon, Anda Degeratu, Frédéric Rochon
We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natur…
Expanding Kähler-Ricci solitons coming out of Kähler cones
Ronan J. Conlon, Alix Deruelle
We give necessary and sufficient conditions for a Kähler equivariant resolution of a Kähler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a…
The moduli space of asymptotically cylindrical Calabi-Yau manifolds
Ronan J. Conlon, Rafe Mazzeo, Frédéric Rochon
We prove that the deformation theory of compactifiable asymptotically cylindrical Calabi-Yau manifolds is unobstructed. This relies on a detailed study of the Dolbeault-Hodge theor…
On the smoothability of certain Kähler cones
Ronan J. Conlon
Let be a Fano manifold that may be realised as for some rank holomorphic vector bundle over some Fano manifold .…
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…
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…
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…