Conformal Geometry, and Geometry of Einstein Metrics and Exotic Differentiable Structures

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For a closed differentiable manifold M, a differential invariant of M, called the Yamabe invariant of M, is one of fundamental subjects in conformal geometry. The studies of the Yamabe problem on singular spaces and Yamabe constants are also important. The results of this Research Theme are the following :・Aubin's Lemma for the Yamabe constants of infinite covering spaces.・Positive Mass Theorem for asymptotically flat spaces with singularities.・Computations of the orbifold Yamabe invariant.・Proof that any closed 3-manifold with positive flat conformal structure is Kleinian.・The solvability of the Yamabe Problem on conic spaces.