Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Shelukhin, Egor"'
We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Ess
Externí odkaz:
http://arxiv.org/abs/2408.08854
Autor:
Shelukhin, Egor
We prove new cases of the Hilbert-Smith conjecture for actions by natural homeomorphisms in symplectic topology. Specifically, we prove that the group of $p$-adic integers $\mathbb Z_p$ does not admit non-trivial continuous actions by Hamiltonian hom
Externí odkaz:
http://arxiv.org/abs/2403.07195
Autor:
Kawamoto, Yusuke, Shelukhin, Egor
Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this setting wh
Externí odkaz:
http://arxiv.org/abs/2310.19033
Autor:
Shelukhin, Egor, Zhang, Jun
We prove that if the $m$-th homotopy group for $m \geq 2$ of a closed manifold has non-trivial invariants or coinvariants under the action of the fundamental group, then there exist infinitely many geometrically distinct closed geodesics for a $C^4$-
Externí odkaz:
http://arxiv.org/abs/2307.13877
Autor:
Buhovsky, Lev, Polterovich, Iosif, Polterovich, Leonid, Shelukhin, Egor, Stojisavljević, Vukašin
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical prediction that the count of zeros of holomorphic self-mappings of the complex linear space should be controlled by the maximum modulus function. We prove
Externí odkaz:
http://arxiv.org/abs/2307.02937
Autor:
Buhovsky, Lev, Payette, Jordan, Polterovich, Iosif, Polterovich, Leonid, Shelukhin, Egor, Stojisavljević, Vukašin
Courant's theorem implies that the number of nodal domains of a Laplace eigenfunction is controlled by the corresponding eigenvalue. Over the years, there have been various attempts to find an appropriate generalization of this statement in different
Externí odkaz:
http://arxiv.org/abs/2206.06347
We prove a number of new results on the large-scale geometry of the $L^p$-metrics on the group of area-preserving diffeomorphisms of each orientable surface. Our proofs use in a key way the Fulton-MacPherson type compactification of the configuration
Externí odkaz:
http://arxiv.org/abs/2105.04658
Autor:
Polterovich, Leonid, Shelukhin, Egor
We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equi
Externí odkaz:
http://arxiv.org/abs/2102.06118
Autor:
Atallah, Marcelo S., Shelukhin, Egor
In 2002 Polterovich has notably established that on closed aspherical symplectic manifolds, Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must in fact be trivial. In this paper we prove the first higher-dimensional H
Externí odkaz:
http://arxiv.org/abs/2008.11758
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