Related papers: Isosystolic Inequalities for Holomorphic Chains in…

The k-systole of a Riemannian manifold is the infimum of the volume over all homologically non-trivial k-cycles. In this paper we discuss the behavior of the dimension two and co-dimension two systole of the complex projective space for…

In this article we completely describe the existence of canonical metrics, known as optimal symplectic connections, on isotrivial K\"ahler fibrations. In this setting an optimal symplectic connection is induced from a Hermite--Einstein…

Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic…

We prove that a simpy connected Hermitian Einstein 4-manifold with non-negative sectional curvature is isometric to complex projective space $\mathbb{C}\mathbb{P}^{2}$ with the Fubini-Study metric or isometric to the product…

We study the Fubini-Study currents and equilibrium metrics of continuous Hermitian metrics on sequences of holomorphic line bundles over a fixed compact K\"ahler manifold. We show that the difference between the Fubini-Study currents and…

A given Hamiltonian matrix H with real spectrum is assumed tridiagonal and non-Hermitian. Its possible Hermitizations via an amended, ad hoc inner-product metric are studied. Under certain reasonable assumptions, all of these metrics are…

We establish sharp inequalities for two-dimensional systolic invariants of metrics with positive scalar curvature: the $2$-systole and the spherical $2$-systole of compact K\"ahler manifolds, and the stable $2$-systole of Riemannian metrics…

The aim of this paper is to study pointed Gromov-Hausdorff Convergence of sequences of K\"ahler submanifolds of a fixed K\"ahler ambient space. Our result shows that lower bounds on the scalar curvature imply convergence to a smooth…

In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an…

We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…

We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with the implications of algebro-geometric nature under the existence of a Hermitian metric with nonnegative…

Over a non-archimedean local place, the height of a projective variety with respect to a very ample line bundle equipped with a Fubini-Study metric is related to the naive height of its Chow form. Using a non-Archimedean Kempf-Ness…

Given an ample line bundle $L$ over a projective $\mathbb{K}$-variety $X$, with $\mathbb{K}$ a non-Archimedean field, we study limits of non-Archimedean metrics on $L$ associated to submultiplicative sequences of norms on the graded pieces…

We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to…

It is shown that many results, previously believed to be properties of the Lichnerowicz Ricci curvature, hold for the Ricci curvature of all Gauduchon connections. We prove the existence of $t$--Gauduchon Ricci-flat metrics on the…

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with $s-p$ orbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to…

This paper primarily establishes an asymptotic variance estimate for smooth linear statistics associated with zero sets of systems of random holomorphic sections in a sequence of positive Hermitian holomorphic line bundles on a compact…

We present some results that complement our prequels [arXiv:1809.08425,arXiv:1907.05770] on holomorphic vector bundles. We apply the method of the Quot-scheme limit of Fubini-Study metrics developed therein to provide a generalisation to…

Let $X$ be a compact hyperbolic Riemann surface equipped with the Poincar\'e metric. For any integer $k\geq 2$, we investigate the Bergman kernel associated to the holomorphic Hermitian line bundle $\Omega^{\otimes k}_X$, where $\O$ is the…

Fine and Premoselli (FP) constructed the first examples of manifolds that do not admit a locally symmetric metric but do admit a negatively curved Einstein metric. The manifolds here are hyperbolic branched covers like those used by Gromov…