An application of quaternionic analysis to the solution of time-independent Maxwell equations and of Stokes’ equation
An application of twistor theory to the non-hyperbolicity of certain compact symplectic Kähler manifolds.
An arithmetic Hilbert–Samuel theorem for pointed stable curves
Let be an arithmetic ring of Krull dimension at most and a pointed stable curve. Write . For every integer , the invertible sheaf inherits a singular hermitian structure from the hyperbolic metric on the Riemann surface . In this article we define a Quillen type metric on the determinant line
An Arzela-Ascoli theorem for immersed submanifolds
The classical Arzela-Ascoli theorem is a compactness result for families of functions depending on bounds on the derivatives of the functions, and is of invaluable use in many fields of mathematics. In this paper, inspired by a result of Corlette, we prove an analogous compactness result for families of immersed submanifolds which depends only on bounds on the derivatives of the second fundamental forms of these submanifolds. We then show how the result of Corlette may be obtained as an immediate...
An Eigenvalue Pinching Theorem.
An elementary formula for the Fenchel-Nielsen twist.
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.