相关论文: Singular Monge-Ampere foliations
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
We prove a convex integration result for the Monge-Ampere system in dimension $d=2$ and arbitrary codimension $k\geq 1$. We achieve flexibility up to the Holder regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, improving hence the previous…
This text contains the material discussed by the author in the Bourbaki seminar of June 2018, on the recent developments in the theory of the Monge-Amp\`ere equation.
This article was withdrawn by the arXiv.org administrators since it plagiarizes math.AT/0401211.
In this article, we provide a multilinear version of the H\"ormander multiplier theorem with a Lorentz-Sobolev space condition. The work is motivated by the recent result of the first author and Slav\'ikov\'a where an analogous version of…
In this paper, we investigate the interior H\"older regularity of solutions to the linearized Monge-Amp\`ere equation. In particular, we focus on the cases with singular right-hand side, which arise from the study of the semigeostrophic…
In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.
Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!
This paper has been withdrawn. See v1 still available to understand the problem: Proposition 2.2 is false. The error in the proof is in claim (3). Then, the whole paper collapses. We do not have any correction for now. We apologize to…
We give a new simpler proof of a theorem of Jayne and Rogers.
Minor technical changes. Section 4 improved.
This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.
In this paper we correct the errors of Yu.~N.~Kuznetsova's paper on the continuous duality for Moore groups.
We corrected a few errors in the previous submission. These do not affect any of the topological conclusions of the earlier version. We have also included a few observations about the Casson invariant of the Brieskorn homology spheres.
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
We study continuity properties of generalized Monge-Amp\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a…
In this paper, we prove the asymptotic expansion of the solutions to some singular complex Monge-Amp\`ere equation which arise naturally in the study of the conical K\"ahler-Einstein metric.
We consider the complex Monge-Amp\`ere equation on a compact K\"ahler manifold $(M, g)$ when the right hand side $F$ has rather weak regularity. In particular we prove that estimate of $\t\phi$ and the gradient estimate hold when $F$ is in…