Related papers: Counterexamples to the pseudo-Riemannian Lichnerow…

This paper has been withdrawn by the authors due to an error in Section 7.

The paper by G. Liu [arxiv:2109.02561] contains an error. In this note, I give a brief review of the problem and indicate what the error is.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

Error in proof of theorem 10.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

We reply to the "Comment on 'The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors'" [arXiv:1604.06432]. We believe the comment misrepresents our papers, and fails to provide a plausible resolution to…

The Lp-Brunn-Minkowski inequality palys a central role in the Brunn-Minkowski theory proposed by Firey [13] in 60's and developed by Lutwak [26,27] in 90's, which generalizes the classical Brunn-Minkowski inequality by Lp-sum of convex…

In this paper, we confirm two conjectures proposed by Georgiev, G\'{o}mez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$, thereby providing a complete solution to the de Bruin--Sharma problem. We further…

We prove a degenerate homological Arnol'd conjecture on Lagrangian intersections beyond the case studied by A. Floer and H. Hofer via a new version of Lagrangian Ljusternik--Schnirelman theory. We introduce the notion of (Lagrangian)…

The comment gives principal arguments proving that the claims given in the title of the commented paper and some its conclusions have to be wrong for principal reasons. An example illustrating the arguments is provided via atomistic…

I reassess the gedankenexperiment of Greenberger, Horne, Shimony and Zeilinger after twenty-five years, finding their influential claim to discovery of an inconsistency inherent in high dimensional formulations of local realism to arise…

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2

Paper withdrawn by the author.

In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…

We show that the uniform Littlewood Conjecture (ULC) recently introduced by Bandi, Fregoli and Kleinbock is false. More precisely the counterexamples form a residual set, the method further suggests positive Hausdorff dimension. For a…

What have become known as the "Darmois" and "Lichnerowicz" junction conditions are often stated to be equivalent, "essentially" equivalent, in a "sense" equivalent, and so on. One even sees not infrequent reference to the…

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

We show how to deduce the standard sign conjecture (a weakening of the K\"unneth standard conjecture) for Shimura varieties from some statements about discrete automorphic representations (Arthur's conjectures plus a bit more). We also…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.