Related papers: Calabi type functionals for coupled K\"ahler-Einst…

In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated…

It is shown that a compact $n$-dimensional K\"ahler manifold with $\frac{n}{2}$-positive Calabi curvature operator has the rational cohomology of complex projective space. For even $n,$ this is sharp in the sense that the complex quadric…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We compute the exact two-sphere partition function and matrix of two-point functions of operators in the chiral ring with their complex conjugates in two-dimensional supersymmetric gauge theories. For gauge theories that flow in the…

This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and…

Non K\"ahler Calabi Yau theory is a newly developed subject and it arises naturally in mathematical physics and generalized geometry. The relevant geometrics are pluriclosed metrics which are critical points of the generalized Einstein…

Henkin functionals on non-commutative $\mathrm{C}^*$-algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our aim in this paper is characterize these functionals through…

Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a best possible constant factor related to the Hurwitz zeta…

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…

We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled…

In this note we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono, gives rise to new conformally K\"ahler, Einstein-Maxwell metrics. The correspondent K\"ahler metrics are…

Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…

A correction is brought to the opinion expressed in a previous note published in this journal that the off critical line points indicated by some authors as being non trivial zeros of the Davenport and Heilbronn function are affected of…

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing…

We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant…

In 1978, Yau confirmed a conjecture due to Calabi stating the existence of K\"ahler metrics with prescribed Ricci forms on compact K\"ahler manifolds. A version of this statement for effective orbifolds can be found in the literature. In…

We continue our study of the mixed Einstein-Hilbert action as a functional of a pseudo-Riemannian metric and a linear connection. Its geometrical part is the total mixed scalar curvature on a smooth manifold endowed with a distribution or a…

In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and…

Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the…

We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of inner automorphisms of Courant algebroids. The zero locus of our moment map is given by the solutions of the…