Anna Kiesenhofer
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View article: A b$b$‐symplectic slice theorem
A b$b$‐symplectic slice theorem Open
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theore…
View article: Small data global regularity for half-wave maps in <i>n</i> = 4 dimensions
Small data global regularity for half-wave maps in <i>n</i> = 4 dimensions Open
We prove that the half-wave maps problem on with target S 2 is globally well-posed for smooth initial data which are small in the critical l 1 based Besov space. This is a formal analogue of the result proved by Tataru for wave maps.
View article: A b-symplectic slice theorem
A b-symplectic slice theorem Open
Eva Miranda is supported by the Catalan institution for Research and Advanced Studies via an ICREA AcademiaPrize 2016. Roisin Braddell is supported by a predoctoral grant from UPC with the ICREA Academia project of EvaMiranda. Roisin Brad…
View article: b-Structures on Lie groups and Poisson reduction
b-Structures on Lie groups and Poisson reduction Open
We introduce the notion of $b$-Lie group as a pair $(G,H)$ where $G$ is a Lie group and $H$ is a codimension-one Lie subgroup, and study the associated canonical $b$-symplectic structure on the $b$-cotangent bundle $^b {T}^\ast G$ together…
View article: Small data global regularity for half-wave maps in $n = 4$ dimensions
Small data global regularity for half-wave maps in $n = 4$ dimensions Open
We prove that the half-wave maps problem on $\mathbb{R}^{4+1}$ with target $S^2$ is globally well-posed for smooth initial data which are small in the critical $l^1$ based Besov space. This is a formal analogue of the result for wave maps …
View article: Cotangent models for group actions on $b$-Poisson manifolds
Cotangent models for group actions on $b$-Poisson manifolds Open
In this article we give a normal form of a $b$-symplectic form in the neighborhood of a compact orbit of a Lie group action on a $b$-symplectic manifold. We establish cotangent models for Poisson actions on $b$-Poisson manifolds and a $b$-…
View article: A $b$-symplectic slice theorem
A $b$-symplectic slice theorem Open
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of $b$-symplectic manifolds started in [12], we prove a slice theorem for Lie group actions on $b$-symplectic manifolds.
View article: Integrable systems on b-symplectic manifolds
Integrable systems on b-symplectic manifolds Open
The study of b-symplectic manifolds was initiated in 2012 by the works of Victor Guillemin, Eva Miranda and Ana Rita Pires (Adv. Math. 264 (2014), 864¿896). These manifolds, which can be understood as symplectic manifolds with singularitie…
View article: Noncommutative integrable systems on b-symplectic manifolds
Noncommutative integrable systems on b-symplectic manifolds Open
In this paper we study non-commutative integrable systems on $b$-Poisson\nmanifolds. One important source of examples (and motivation) of such systems\ncomes from considering non-commutative systems on manifolds with boundary\nhaving the r…
View article: Cotangent models for integrable systems on $b$-symplectic manifolds
Cotangent models for integrable systems on $b$-symplectic manifolds Open
In this paper we give cotangent models for integrable systems in symplectic
and $b$-symplectic manifolds. The proof of the existence of such (semilocal)
models boils down to the corresponding action-angle coordinate theorems in
these setti…
View article: Cotangent models for integrable systems
Cotangent models for integrable systems Open
We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on a special class called $b$-Poisson/$b$-symplectic manifolds. The semilocal equivalence with such models uses the correspo…