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math.DG2026
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.
math.DG2026
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…
math.DG2026
PIC1 pinched manifolds are flat or compact
Alix Deruelle, Man-Chun Lee, Felix Schulze +2
Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this pa…