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We de ne higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This...
A Fatou–Bieberbach domain avoiding a neighborhood of a variety of codimension 2.
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere Sn+d under integral curvature conditions. As a consequence, we obtain several di...
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere $\mathbb{S}^{n+d}$ under integral curvature conditions. As a consequence, we obt...
In this paper we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms. Particularly, we prove that the mean curvature flow deforms a...
In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension d 1, which generalizes the extension t...
Abstract: In this paper, we continue the study of which $h$-vectors $\H=(1,3,..., h_{d-1}, h_d, h_{d+1})$ can be the Hilbert function of a level algebra by investigating Artinian level algebras of cod...
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.MSC 2010: Primary 53C44.
This paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of quadratic codimension-four centers $Q_4$. Gavrilov and Iliev set an upper bound of {\it eight} for th...
We prove Ma˜n´e’s conjectures ([Mn96]) in the context of codimension one Aubry-Mather theory
This work is part of the Graded Ring Database project [GRDB],and is a sequel to [A0], [A] and [ABR]. We introduce a strategy based on KustinMiller unprojection [KM].
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds,those equipped with a closed one-form defining the symplectic foliation and a closed ...
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori esti...

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