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Notes on the uniqueness of Type II Yamabe metrics
Shota Hamanaka, Pak Tung Ho
In this paper, we study the uniqueness of type II Yamabe metrics in conformal classes on a compact connected manifold with boundary, and we investigate Obata-type theorems for type…
Extremal metrics involving scalar curvature
Shota Hamanaka
We investigate extremal metrics at which various types of rigidity theorems involving scalar curvatures hold. The rigidity we discuss here is related to the rigidity theorems prese…
Notes on scalar curvature lower bounds of steady gradient Ricci solitons
Shota Hamanaka
We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose $\in…
Upper bound preservation of the total scalar curvature in a conformal class
Shota Hamanaka
We show that in an arbitrarily fixed conformal class with non-positive Yamabe constant on a closed manifold, the upper bound of the total scalar curvature is preserved under the $C…
Limit theorems for the total scalar curvature
Shota Hamanaka
We study some preservation phenomena for lower bound of total scalar curvatures on a smooth manifold. In particular, we prove that the lower bound of the weighted total scalar curv…
Type of finite time singularities of the Ricci flow with bounded scalar curvature
Shota Hamanaka
In this paper, we study the Ricci flow on a closed manifold of dimension and finite time interval on which the scalar curvature are uniformly bounded…
Ricci flow with bounded curvature integrals
Shota Hamanaka
In this paper, we study the Ricci flow on a closed manifold and finite time interval on which certain integral curvature energies are finite. We prove that in…
Non-Einstein relative Yamabe metrics
Shota Hamanaka
In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relativ…
Decompositions of the space of Riemannian metrics on a compact manifold with boundary
Shota Hamanaka
In this paper, for a compact manifold with non-empty boundary, we give a Koiso-type decomposition theorem, as well as an Ebin-type slice theorem, for the space of all Riemannia…