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arXiv · 1901.01647

Disjoint superheavy subsets and fragmentation norms

Morimichi Kawasaki·Ryuma Orita
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Abstract

We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding $I\colon \mathbb{R}^n\to\mathrm{Ham}(M)$ with respect to the fragmentation norm on the group $\mathrm{Ham}(M)$ of Hamiltonian diffeomorphisms of a symplectic manifold $(M,\omega)$. As an application, we provide an answer to Brandenbursky's question on fragmentation norms on $\mathrm{Ham}(\Sigma_g)$, where $\Sigma_g$ is a closed Riemannian surface of genus $g\geq 2$

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Morimichi Kawasaki, Ryuma Orita. 2019-01-07. Disjoint superheavy subsets and fragmentation norms. https://arxiv.org/abs/1901.01647

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