Related papers: On a conjecture by Blocki-Zwonek
Further experiments showed the incorrectness of proposed interpretation.
We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.
We give a counterexample to the generalized Bogomolov-Gieseker inequality for threefolds conjectured by Bayer, Macr\`i and Toda using the blow up of a point over three dimensional projective space.
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].
We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.
We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.
We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".
We prove a variation of Gronwall's lemma.
In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named author in 1978.
We prove some extensions of Andrews inequality.
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).
We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a different construction, and gives new ones in all other dimensions…
In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.
We prove Union-Closed sets conjecture.
We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…
The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.
We prove a conjecture due to Y. Last on Jacobi matrices.