Zobrazeno 1 - 10
of 134
pro vyhledávání: '"Abbondandolo, Alberto"'
We prove that all normalized symplectic capacities coincide on smooth domains in $\mathbb C^n$ which are $C^2$-close to the Euclidean ball, whereas this fails for some smooth domains which are just $C^1$-close to the ball. We also prove that all symp
Externí odkaz:
http://arxiv.org/abs/2312.07363
We consider general classes of gradient models on regular trees with values in a countable Abelian group $S$ such as $\mathbb{Z}$ or $\mathbb{Z}_q$, in regimes of strong coupling (or low temperature). This includes unbounded spin models like the p-SO
Externí odkaz:
http://arxiv.org/abs/2302.05398
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric questions arising in this context concerning distance, geodesics and their
Externí odkaz:
http://arxiv.org/abs/2210.02387
Publikováno v:
Journal de l'\'Ecole polytechnique - Math\'ematiques 9 (2022), 807-851
A contact form is called Besse when the associated Reeb flow is periodic. We prove that Besse contact forms on closed connected 3-manifolds are the local maximizers of suitable higher systolic ratios. Our result extends earlier ones for Zoll contact
Externí odkaz:
http://arxiv.org/abs/2107.12138
Publikováno v:
Sel. Math. New Ser. 29, 67 (2023)
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arbitrarily small topological entropy. In contrast, for many closed manifolds there is a uniform positive lower bound for the topological entropy of (not
Externí odkaz:
http://arxiv.org/abs/2103.01144
Autor:
Abbondandolo, Alberto, Rot, Thomas O.
Publikováno v:
Topol. Methods Nonlinear Anal. 59 (2022), 585-621
In a previous paper we classified the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold to its model space in terms of a suitable version of framed cobordism. We explicitly computed these homotopy classes for non-
Externí odkaz:
http://arxiv.org/abs/2005.03936
Autor:
Abbondandolo, Alberto, Majer, Pietro
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of Morse-Smale diffe
Externí odkaz:
http://arxiv.org/abs/2003.07134
Publikováno v:
Geom. Funct. Anal. (GAFA) 33 (2023), 299-363
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this result are: (i) sharp local systolic inequalities for Riemannian an
Externí odkaz:
http://arxiv.org/abs/1912.04187
Autor:
Abbondandolo, Alberto, Kang, Jungsoo
Publikováno v:
Duke Math J. 171 (2022), 739-830
We prove that the Floer complex that is associated with a convex Hamiltonian function on $\mathbb{R}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated with the Fenchel-dual Hamiltonian. This isomorphism pr
Externí odkaz:
http://arxiv.org/abs/1907.07779