Related papers: Nakamaye's theorem on complex manifolds
We prove an extension theorem for Kahler currents with analytic singularities in a Kahler class on a complex submanifold of a compact Kahler manifold.
We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it.…
In this paper we use a dynamical approach to prove some new divergence theorems on complete non-compact Riemannian manifolds.
We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge-Riemann theorem for compact Kaehler manifolds.
We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.
In this paper, we consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.
We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in…
We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We generalize the Cauchy-Davenport theorem to locally compact groups.
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…
We prove several approximation theorems of the complex Monge-Ampere operator on a compact Kahler manifold. As an application we give a new proof of a recent result of Guedj and Zeriahi on a complete description of the range of the complex…
In this paper, we present extensions of the classical Bonnet-Myers theorem for Riemannian manifolds with nonnegative Ricci curvature. Our results provide criteria for compactness and a method for estimating the diameter of such manifolds…
The Kakimizu complex is usually defined in the context of knots, where it is known to be quasi-Euclidean. We here generalize the definition of the Kakimizu complex to surfaces and 3-manifolds (with or without boundary). Interestingly, in…
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…
A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved. Applications to twistor theory are discussed.
The Kodaira-Nakano Vanishing Theorem has been generalized to the relative setting by A. Sommese. We prove a version of this theorem for non-compact manifolds. As an apllication, we prove that the cohomology of a fiber of a symplectic…