Related papers: On the DDVV Conjecture and the Comass in Calibrate…

In this paper, we proved P(n,3), which is an important part of the DDVV conjecture. The general case will be treated in the next version of the paper.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

In this paper, we give a proof of the DDVV conjecture which is a pointwise inequality involving the scalar curvature, the normal scalar curvature and the mean curvature on a submanifold of a real space form. Furthermore we solved the…

In this note we give a survey on the DDVV conjecture which is also called the "normal scalar curvature conjecture".

In this paper, we investigate the DDVV-type inequality for Riemannian maps from quaternionic space forms to Riemannian manifolds. We also discuss the equality case of the derived inequality with application.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The article presents the proof of Casas-Alvero conjecture.

Two conjectures recently proposed by one of the authors are disproved

The paper aims to point out a novel geometric characterisation of the WDVV equations of 2D topological field theory.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

In this paper the circulant Hadamard conjecture is proved.

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We show that the Jacobian conjecture of the two dimensional case is true.

This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

In this article, following an insight of Kontsevich, we extend the famous Weil conjecture (as well as the strong form of the Tate conjecture) from the realm of algebraic geometry to the broad noncommutative setting of dg categories. As a…