4 papers
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…