An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties.
An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties
An equality for the curvature function of a simple and closed curve on the plane.
An equichordal characterization of round spheres.
An equivalence theorem for submanifolds of higher codimensions
For a submanifold of of any codimension the notion of type number is introduced. Under the assumption that the type number is greater than 1 an equivalence theorem is proved.
An equivalent flat condition.
An Equivariant Pniching Theorem.
An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere.
An example of a 6-dimensional flat almost Hermitian manifold
An example of an almost hyperbolic Hermitian manifold.
An example of an asymptotically Chow unstable manifold with constant scalar curvature
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
An example of Lie group with Sasakian structure of constant -sectional curvature.
An excess sphere theorem
An exhaustion of locally symmetric spaces by compact submanifolds with corners.
An existence result for minimal spheres in manifolds boundary
We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
An Existence Theorem for Harmonic Maps.
An existence theorem for the Yamabe problem on manifolds with boundary
Let be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.
An exotic smooth structure on .
An explicit classification of 3-dimensional Riemannian spaces satisfying
An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times