Related papers: Counterexamples to the pseudo-Riemannian Lichnerow…
This paper has been withdrawn by the author, due to a crucial error in page 5.
We construct the first known examples of compact pseudo-Riemannian manifolds having an essential group of conformal transformations, and which are not conformally flat. Our examples cover all types $(p,q)$, with $2 \leq p \leq q$.
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
In this note, we disprove two Romanov type conjectures posed by Chen.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament's Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden.
The paper has been withdrawn by the author due to a crucial error.
We prove an important partial case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the round sphere (up to a finite…
Recently GM Sofi & SA Shabir [arXive: 1903.01850v2 [math.GM] 6 Mar 2019] made an attempt to prove the Sendov's conjecture. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.
Lorentzian versions of classical Riemannian volume comparison theorems by Gunther, Bishop and Bishop-Gromov, are stated for suitable natural subsets of general semi-Riemannian manifolds. The problem is more subtle in the Bishop-Gromov case,…
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
This paper has been withdrawn by the author due to a crucial argument error at p.10.
WITHDRAWN: The proof contains an uncorrectable gap in the proof of theorem 7 on page 11. A proof of the Krzyz conjecture is presented, based on the application of the variational method, as well as on the use of two classical results and…
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
It is shown that the claims expressed in the Comment arXiv:0810.3247v1 against my paper Phys. Rev. Lett. {\bf 101}, 163603 (2008) [arXiv:0809.3901] are obviously wrong or not essential.
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
The paper presents a counterexample to the Hodge conjecture.