29 citations · 106 across the 33 of their papers we have counts for
9 papers · 1 filter
Simple proof of the global inverse function theorem via the Hopf--Rinow theorem
Shinobu Ohkita, Masaki Tsukamoto
We explain that Hadamard's global inverse function theorem very simply follows from the Hopf--Rinow theorem in Riemannian geometry.
Large dynamics of Yang--Mills theory: mean dimension formula
Masaki Tsukamoto
This paper studies the Yang--Mills ASD equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution…
Local mean dimension of ASD moduli spaces over the cylinder
Shinichiroh Matsuo, Masaki Tsukamoto
We study an infinite dimensional ASD moduli space over the cylinder. Our main result is the formula of its local mean dimension. A key ingredient of the argument is the notion of n…
Sharp lower bound on the curvatures of ASD connections over the cylinder
Masaki Tsukamoto
We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.
An open four-manifold having no instanton
Masaki Tsukamoto
Taubes proved that all compact oriented four-manifolds admit non-flat instantons. We show that there exists a non-compact oriented four-manifold having no non-flat instanton.
Instanton approximation, periodic ASD connections, and mean dimension
Shinichiroh Matsuo, Masaki Tsukamoto
We study a moduli space of ASD connections over . We consider not only finite energy ASD connections but also infinite energy ones. So the moduli space is inf…