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math.SG2019★ 1 cited
A Comparison between Hofer's metric and C^1-topology
Yoshihiro Sugimoto
Hofer's metric is a bi-invariant metric on Hamiltonian diffeomorphism groups. Our main result shows that the topology induced from Hofer's metric is weaker than C^1-topology if the…
math.DG2019
Applications of square roots of diffeomorphisms
Yoshihiro Sugimoto
In this paper, we prove that on any contact manifold, there exists an arbitrary C^{\infty}-small contactomorphism which does not admit a square root. In particular, there exists an…
math.SG2019★ 2 cited
The sharp energy-capacity inequality on convex symplectic manifolds
Yoshihiro Sugimoto
In symplectic geometry, symplectic invariants are useful tools in studying symplectic phenomena. Hofer-Zehnder capacity and displacement energy are important symplectic invariants.…