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math.DG2025
Linear stability and instability of Kähler Ricci solitons
Keaton Naff, Tristan Ozuch
We show that the recently discovered BCCD shrinking soliton is linearly unstable, by extending the approach of \cite{chi04} and \cite{hm11}, via recent work the \cite{cm21} on grad…
math.DG2025
Ricci Flow on ALF manifolds
Dain Kim, Tristan Ozuch
We prove that on ALF -manifolds with the Ricci flow preserves the ALF structure, and develop a weighted Fredholm framework adapted to ALF manifolds. Motivated by Perelm…
math.DG2025
Linear stability of the blowdown Ricci shrinker in 4D
Keaton Naff, Tristan Ozuch
We prove that the four-dimensional blowdown shrinking Ricci soliton constructed by Feldman-Ilmanen-Knopf is strictly linearly stable in the sense of Cao-Hamilton-Ilmanen. This prov…