Related papers: A survey on the DDVV conjecture

In this short essay, we will survey on two conjectures in non-K\"ahler geometry: the constant holomorphic sectional curvature conjecture and the Fino-Vezzoni conjecture. We aim at the broad audience and assume no expertise in non-K\"ahler…

We prove a criterion of existence of solutions conjectured by C. C. Chen and C. S. Lin [20] for the prescribed scalar curvature problem on the standard n-dimensional sphere.

This is a survey on Kawaguchi-Silverman conjecture.

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.

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.

The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties…

We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in $KK$-theory. These notes serve as an intuitive guide to these results, avoiding the necessary technical proofs. We…

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to…

In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.

We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.

We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.

We present a new approach for averaging in general relativity and cosmology. After a short review of the theory originally taken from the equivalence problem, we consider two ways how to deal with averaging based on Cartan scalars. We apply…

Inspired by [Qiu, Wilson 2019] and [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Delta Square], we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in [Haglund, Sergel 2019] to obtain a…

In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…

The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivial if and only if the knot is trivial. We will use…

In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…

Wintgen ideal submanifolds in space forms are those ones attaining equality pointwise in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the scalar normal curvature. They are Moebius invariant…