5 papers
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…
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…
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…
Upper bound preservation of the total scalar curvature in a conformal class
Shota Hamanaka
We show that in an arbitrarily fixed conformal class on a closed manifold, the upper bound condition of the total scalar curvature is -closed if its Yamabe constant is nonpo…