2 citations · 2 across the 9 of their papers we have counts for
10 papers
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…
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…
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…
Orbifold singularity formation along ancient and immortal Ricci flows
Alix Deruelle, Tristan Ozuch
In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension with Einstein orbifolds as tangent flows at infinity. For ins…
Ancient and expanding spin ALE Ricci flows
Isaac M. Lopez, Tristan Ozuch
We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity…
Families of degenerating Poincaré-Einstein metrics on
Carlos A. Alvarado, Tristan Ozuch, Daniel A. Santiago
We provide the first example of continuous families of Poincaré-Einstein metrics developing cusps on the trivial topology . We also exhibit families of metrics with u…
Dynamical (in)stability of Ricci-flat ALE metrics along Ricci flow
Alix Deruelle, Tristan Ozuch
We study the stability and instability of ALE Ricci-flat metrics around which a Lojasiewicz inequality is satisfied for a variation of Perelman's -functional adapted to the ALE…
Depth separation beyond radial functions
Luca Venturi, Samy Jelassi, Tristan Ozuch +1
High-dimensional depth separation results for neural networks show that certain functions can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer o…
A Łojasiewicz inequality for ALE metrics
Alix Deruelle, Tristan Ozuch
We introduce a new functional inspired by Perelman's -functional adapted to the asymptotically locally Euclidean (ALE) setting and denoted . Its expressi…
Perelman's functionals on cones and Construction of type III Ricci flows coming out of cones
Tristan Ozuch
In this paper, we are interested in conical structures of manifolds with respect to the Ricci flow and, in particular, we study them from the point of view of Perelman's functional…