Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Deruelle, Alix"'
Autor:
Deruelle, Alix, Ozuch, Tristan
In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension $4$ with Einstein orbifolds as tangent flows at infinity. For instance, for any $k\in\mathbb{N}_0$, we obtain continuous families of no
Externí odkaz:
http://arxiv.org/abs/2410.16075
We study $n$-dimensional Ricci flows with non-negative Ricci curvature where the curvature is pointwise controlled by the scalar curvature and bounded by $C/t$, starting at metric cones which are Reifenberg outside the tip. We show that any such flow
Externí odkaz:
http://arxiv.org/abs/2403.00708
We prove the existence of a unique complete shrinking gradient K\"ahler-Ricci soliton with bounded scalar curvature on the blowup of $\mathbb{C}\times\mathbb{P}^{1}$ at one point. This completes the classification of such solitons in two complex dime
Externí odkaz:
http://arxiv.org/abs/2206.10785
Let $D$ be a toric K\"ahler-Einstein Fano manifold. We show that any toric shrinking gradient K\"ahler-Ricci soliton on certain toric blowups of $\mathbb{C}\times D$ satisfies a complex Monge-Amp\`ere equation. We then set up an Aubin continuity path
Externí odkaz:
http://arxiv.org/abs/2205.08482
This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to t
Externí odkaz:
http://arxiv.org/abs/2203.15313
We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient K\"ahler-Ricci soliton $(M,\,g,\,X)$ with soliton metric $g$ with bounded scalar curvature $\operatorname{R}_{g}$ whose soliton vecto
Externí odkaz:
http://arxiv.org/abs/2203.04380
Autor:
Deruelle, Alix, Ozuch, Tristan
We study the stability and instability of ALE Ricci-flat metrics around which a Lojasiewicz inequality is satisfied for a variation of Perelman's $\lambda$-functional adapted to the ALE situation and denoted $\lambda_{\operatorname{ALE}}$. This funct
Externí odkaz:
http://arxiv.org/abs/2104.10630
Autor:
Deruelle, Alix, Schulze, Felix
We prove an optimal relative integral convergence rate for two expanding gradient Ricci solitons coming out of the same cone. As a consequence, we obtain a unique continuation result at infinity and we prove that a relative entropy for two such self-
Externí odkaz:
http://arxiv.org/abs/2101.02638
Autor:
Deruelle, Alix, Ozuch, Tristan
We introduce a new functional inspired by Perelman's $\lambda$-functional adapted to the asymptotically locally Euclidean (ALE) setting and denoted $\lambda_{\operatorname{ALE}}$. Its expression includes a boundary term which turns out to be the ADM-
Externí odkaz:
http://arxiv.org/abs/2007.09937
Autor:
Conlon, Ronan J., Deruelle, Alix
We show that, up to the flow of the soliton vector field, there exists a unique complete steady gradient K\"ahler-Ricci soliton in every K\"ahler class of an equivariant crepant resolution of a Calabi-Yau cone converging at a polynomial rate to Cao's
Externí odkaz:
http://arxiv.org/abs/2006.03100