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pro vyhledávání: '"Conlon, Ronan"'
In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\"ahler-Ricci soliton on $\mathbb{C}^{n}$ and asked whether every steady gradient K\"ahler-Ricci soliton of positive curvature on $\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (a
Externí odkaz:
http://arxiv.org/abs/2403.04089
Autor:
Conlon, Ronan J., Rochon, Frédéric
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 detailed description of the geometry at infinity of these metrics is
Externí odkaz:
http://arxiv.org/abs/2308.02155
Autor:
Conlon, Ronan T.
Publikováno v:
Strategic HR Review, 2024, Vol. 23, Issue 4, pp. 141-146.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/SHR-03-2024-0019
We prove the existence of a unique complete shrinking gradient K\"ahler-Ricci soliton with bounded scalar curvature on the blowup of $\mathbb{C}\times\mathbb{P}^{1}$ at one point. This completes the classification of such solitons in two complex dime
Externí odkaz:
http://arxiv.org/abs/2206.10785
Let $D$ be a toric K\"ahler-Einstein Fano manifold. We show that any toric shrinking gradient K\"ahler-Ricci soliton on certain toric blowups of $\mathbb{C}\times D$ satisfies a complex Monge-Amp\`ere equation. We then set up an Aubin continuity path
Externí odkaz:
http://arxiv.org/abs/2205.08482
We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient K\"ahler-Ricci soliton $(M,\,g,\,X)$ with soliton metric $g$ with bounded scalar curvature $\operatorname{R}_{g}$ whose soliton vecto
Externí odkaz:
http://arxiv.org/abs/2203.04380
Autor:
Conlon, Ronan J., Hein, Hans-Joachim
A Riemannian cone $(C, g_C)$ is by definition a warped product $C = \mathbb{R}^+ \times L$ with metric $g_C = dr^2 \oplus r^2 g_L$, where $(L,g_L)$ is a compact Riemannian manifold without boundary. We say that $C$ is a Calabi-Yau cone if $g_C$ is a
Externí odkaz:
http://arxiv.org/abs/2201.00870
Autor:
Conlon, Ronan J., Deruelle, Alix
We show that, up to the flow of the soliton vector field, there exists a unique complete steady gradient K\"ahler-Ricci soliton in every K\"ahler class of an equivariant crepant resolution of a Calabi-Yau cone converging at a polynomial rate to Cao's
Externí odkaz:
http://arxiv.org/abs/2006.03100
Publikováno v:
Geom. Topol. 28 (2024) 267-351
We first show that a K\"ahler cone appears as the tangent cone of a complete expanding gradient K\"ahler-Ricci soliton with quadratic curvature decay with derivatives if and only if it has a smooth canonical model (on which the soliton lives). This a
Externí odkaz:
http://arxiv.org/abs/1904.00147
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