Related papers: A short note on Godbersen's Conjecture
The long-standing Godbersen's conjecture asserts that the Rogers-Shephard inequality for the volume of the difference body is refined by an inequality for the mixed volume of a convex body and its reflection about the origin. The conjecture…
Two new proofs are provided, offering two new perspectives on Godbersen's conjecture. One of the proofs utilizes Helly's theorem to provide a concise and elegant proof of the inequality in Godbersen's conjecture. The other proof utilizes…
The longstanding Godbersen's conjecture states that for any convex body $K \subset \mathbb R^n$ of volume $1$ and any $j \in \{0, \ldots, n\}$, the mixed volume $V_j = V(K[j], -K[n - j])$ is bounded by $\binom{n}{j}$, with equality if and…
We survey recent developments on the Restriction conjecture.
We provide a natural generalization of a geometric conjecture of F\'{a}ry and R\'{e}dei regarding the volume of the convex hull of $K \subset {\mathbb R}^n$, and its negative image $-K$. We show that it implies Godbersen's conjecture…
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
In this note we give a short proof of Godbersen's conjecture for the class of locally anti-blocking bodies. We show that all equality cases amongst locally anti-blocking bodies are for simplices, further supporting the conjecture. The proof…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
New cases of the multiplicity conjecture are considered.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)] is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the…
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
The paper presents a counterexample to the Hodge conjecture.
This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We improve constants in the Rademacher-Menchov inequality.
We report the finding of the new upper bound on the lowest positive integer $x$ for which the Mertens conjecture \begin{equation*} \left| \sum_{1 \leq n \leq x} \mu(n) \right| < \sqrt{x} \end{equation*} fails to hold: $x < \exp(1.017 \times…