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Creators/Authors contains: "Deruelle, Alix"

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  1. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Let 𝐷 be a toric Kähler–Einstein Fano manifold. We show that any toric shrinking gradient Kähler–Ricci soliton on certain toric blowups of C×D satisfies a complex Monge–Ampère equation. We then set up an Aubin continuity path to solve this equation and show that it has a solution at the initial value of the path parameter. This we do by implementing another continuity method. 
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  2. ; ; (, Journal of the European Mathematical Society)
    We show that the underlying complex manifold of a complete non-compact two-dimensional shrinking gradient Kähler-Ricci soliton (M,g,X) with soliton metric g with bounded scalar curvature Rg whose soliton vector field X has an integral curve along which Rg↛0 is biholomorphic to either C×P1 or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the Feldman-Ilmanen-Knopf conjecture for finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension. 
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  3. ; ; ; (, Geometric and Functional Analysis)
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  4. ; (, ArXivorg)
    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 resolution of a Calabi-Yau cone converging at a polynomial rate to Cao's steady gradient Kähler-Ricci soliton on the cone. 
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    Accepted Manuscript Full Text Available