Related papers: Almost K\"ahler Kodaira-Spencer problem

We call $n$ a spoof odd perfect number if $n$ is odd and $n=km$ for two integers $k,m>1$ such that $\sigma(k)(m+1)=2n$, where $\sigma$ is the sum-of-divisors function. In this paper, we show how results analogous to those of odd perfect…

We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to $k$-tuples of almost commuting permutations,…

In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled K\"ahler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with…

We consider an almost complex manifold with Norden metric (i. e. a metric with respect to which the almost complex structure is an anti-isometry). On such a manifold we study a linear connection preserving the almost complex structure and…

A hyperK\"ahler potential is a function rho that is a K\"ahler potential for each complex structure compatible with the hyperK\"ahler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperK\"ahler metrics…

We study toric nearly K\"ahler manifolds, extending the work of Moroianu and Nagy. We give a description of the global geometry using multi-moment maps. We then investigate polynomial and radial solutions to the toric nearly K\"ahler…

We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…

Motivated by the results of B. Berndtsson, in this memoir we use the new estimates developed by W. He to extend a theorem of the second author on the existence of weak $C^{1,1}$ geodesics between two smooth non-degenerate K\"ahler…

Using equivalences of categories we provide isomorphisms between the Brauer groups of different Hopf algebras. As an example, we show that when k is a field of characteristic different from 2 the Brauer groups BC(k,H_4,r_t) for every dual…

The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a…

We introduce a "qualitative property" for Bott-Chern cohomology of complex non-K\"ahler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the…

We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some properties of such a constant, as well as of the associated variational problem. We then…

In this paper, we consider the convergence problem of Schr\"odinger equation. Firstly, we show the almost everywhere pointwise convergence of Schr\"odinger equation in Fourier-Lebesgue spaces…

We establish a Rademacher type theorem involving Hamiltonians $H(x,p)$ under very weak conditions in both of Euclidean and Carnot-Carath\'eodory spaces. In particular,$H(x,p)$ is assumed to be only measurable in the variable $x$, and to be…

We develop new algorithms for approximating extremal toric K\"ahler metrics. We focus on an extremal metric on $\mathbb{CP}^{2}\sharp2\overline{\mathbb{CP}}^{2}$, which is conformal to an Einstein metric (the Chen-LeBrun-Weber metric). We…

Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the K\"ahler-Einstein metric attached to (X,D) -whenever it exists- has cone singularities along D on…

We study some properties of pointwise $k$-slant submanifolds of almost Hermitian manifolds with a special view towards K\"{a}hler manifolds. In particular, we characterize the integrability of the component distributions, treating also the…

Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood of the zero section where the adapted complex structure exists. Such neighbourhood is endowed with a canonical…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…