We introduce new invariants of a Riemannian singular space, the local Yamabe and
Sobolev constants, and then go on to prove a general version of the Yamabe theorem under …

We prove a surgery formula for the smooth Yamabe invariant $\sigma (M) $ of a compact
manifold $ M $. Assume that $ N $ is obtained from $ M $ by surgery of codimension at least …

We compare the isoperimetric profiles of S2× R3 and of S3× R2 with that of a round 5-
sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the …

Low-dimensional surgery and the Yamabe invariant Page 1 c 2015 The Mathematical
Society of Japan J. Math. Soc. Japan Vol. 67, No. 1 (2015) pp. 159–182 doi: 10.2969/jmsj/06710159 …

We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of
a compact manifold and the Euclidean space with the flat metric,(M m× R n, g+ g E), m, n> 1 …

Let (M m, g) be a closed Riemannian manifold (m≥ 2) of positive scalar curvature and (N n,
h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant …

AMS :: Sugaku Expositions Skip to Main Content American Mathematical Society American
Mathematical Society MathSciNet Bookstore Publications Publications — Over 100 years of …

We establish a framework for fiberwise symmetrization to find a lower bound of a Dirichlet-
type energy functional in a variational problem on a fibred Riemannian manifold, and use it …

We show that the-equivariant Yamabe invariant of the-sphere, endowed with the Hopf
action, is equal to the (non-equivariant) Yamabe invariant of the-sphere. More generally, we …

We establish a framework for fiberwise spherical or planar symmetrization to find a lower
bound of a Dirichlet-type energy functional in a variational problem on a fibred Riemannian …