Related papers: Singular Monge-Ampere foliations

The aim of this paper is to compare singularities of closed positive currents whose non-pluripolar complex Monge--Amp\`ere masses equal. We also provide a short alternative proof for the monotonicity of non-pluripolar complex…

We explain an error in our paper "A smooth foliation of the 5-sphere by complex surfaces", Ann. Math 156 (2002), p.915-930.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization…

The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…

In a recent paper, Darvas-Rubinstein proved a convergence result for the Kahler-Ricci iteration, which is a sequence of recursively defined complex Monge-Ampere equations. We introduce the Monge-Ampere iteration to be an analogous, but more…

We prove uniform sup-norm estimates for the Monge-Ampere equation with respect to a family of Kahler metrics which degenerate towards a pull-back of a metric from a lower dimensional manifold. This is then used to show the existence of…

The ancillary file Corrigendum.pdf contains an explanation why our proof does not work.

An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.

We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.

The paper is withdrawn due to some errors.

This paper has been withdrawn due to a crucial error in the proof of the main theorem

This paper has been withdrawn due to a missing hypothesis in the main statement.

In this note we make a minor correction to the paper ``Simplicial monoids and Segal categories."

We revisit the convex integration constructions for the Monge-Amp\`ere system and prove its flexibility in dimension $d=2$ and codimension $k=3$, up to $\mathcal{C}^{1,1-1/\sqrt{5}}$. To our knowledge, it is the first result in which the…

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

I withdraw my paper from arXiv because there is a technical error in the proof of Theorem 1.1. And because of this error, all the results in the paper are untrue. I am very sorry for this.

The paper was withdrawn due to a gap in the proof of Lemma 3.

This is a continuation of "Mirror Principle III"(math.AG/9912038).