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pro vyhledávání: '"Gutt, Jean"'
Autor:
Gutt, Jean, Ramos, Vinicius G. B.
It is a long-standing conjecture that all symplectic capacities which are equal to the Gromov width for ellipsoids coincide on a class of convex domains in $\mathbb{R}^{2n}$. It is known that they coincide for monotone toric domains in all dimensions
Externí odkaz:
http://arxiv.org/abs/2312.06476
Chaidez and Edtmair have recently found the first example of dynamically convex domains in $\mathbb R^4$ that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2308.06604
We introduce a new normalization condition for symplectic capacities, which we call cube normalization. This condition is satisfied by the Lagrangian capacity and the cube capacity. Our main result is an analogue of the strong Viterbo conjecture for
Externí odkaz:
http://arxiv.org/abs/2208.13666
We define a transverse Dolbeault cohomology associated to any almost complex structure $j$ on a smooth manifold $M$. This we do by extending the notion of transverse complex structure and by introducing a natural j-stable involutive limit distributio
Externí odkaz:
http://arxiv.org/abs/2208.12668
We investigate the convexity up to symplectomorphism (called symplectic convexity) of star-shaped toric domains in $\mathbb R^4$. In particular, based on the criterion from Chaidez-Edtmair via Ruelle invariant and systolic ratio of the boundary of st
Externí odkaz:
http://arxiv.org/abs/2203.05448
In this article we explore a symplectic packing problem where the targets and domains are $2n$-dimensional symplectic manifolds. We work in the context where the manifolds have first homology group equal to $\mathbb{Z}^n$, and we require the embeddin
Externí odkaz:
http://arxiv.org/abs/2106.10126
A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic capacities agree on convex domains. We also review why
Externí odkaz:
http://arxiv.org/abs/2003.10854
Publikováno v:
Math. Proc. Camb. Phil. Soc. 170 (2021) 625-660
We prove that every non-degenerate Reeb flow on a closed contact manifold $M$ admitting a strong symplectic filling $W$ with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive equivariant
Externí odkaz:
http://arxiv.org/abs/1903.06523
Autor:
Gutt, Jean, Usher, Michael
Publikováno v:
Duke Math. J. 168, no. 12 (2019), 2299-2363
We show that many toric domains $X$ in $R^4$ admit symplectic embeddings $\phi$ into dilates of themselves which are knotted in the strong sense that there is no symplectomorphism of the target that takes $\phi(X)$ to $X$. For instance $X$ can be tak
Externí odkaz:
http://arxiv.org/abs/1708.01574
Autor:
Gutt, Jean, Hutchings, Michael
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 3537-3600
We use positive S^1-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R^{2n}. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but they satisfy axioms which allow the
Externí odkaz:
http://arxiv.org/abs/1707.06514