Related papers: On the Cheltsov--Rubinstein conjecture

In this note, we disprove two Romanov type conjectures posed by Chen.

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

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.

We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.

The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…

The paper presents a counterexample to the Hodge conjecture.

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.

We survey recent developments on the Restriction conjecture.

Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to…

This document collects several approaches attempted in proving the Chen-Raspaud Conjecture for k = 3. Each approach is detailed with full proofs and explanations of why it failed. This compilation aims to provide insights and a foundation…

We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .

Several results about the union-closed sets conjecture are presented.

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.

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.