Related papers: On the Critical Points of the E_k Functionals in K…

We investigate compact complex manifolds endowed with SKT or balanced metrics. In each case we define a new functional whose critical points are proved to be precisely the K\"ahler metrics, if any, on the manifold. As general manifolds of…

In this short note we are concerned with the Kahler-Einstein metrics near cone type log canonical singularities. By two different approaches, we construct a complete Kahler-Einstein metric with negative scalar curvature in a neighborhood of…

In this paper we investigate complete critical metrics of the $L^{2}$-norm of the scalar curvature. We prove that any complete critical metric with positive scalar curvature has constant scalar curvature and we characterize critical metrics…

In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of…

We study the existence of extremal functions on compact Riemannian manifold wich is locally Euclidean .

We apply equivariant localisation to the theory of $Z$-stability and $Z$-critical metrics on a K\"ahler manifold $(X,\alpha)$, where $\alpha$ is a K\"ahler class. We show that the invariants used to determine $Z$-stability of the manifold,…

In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of Hecke polynomials, which are associated with the space of cusp…

In this paper, we show that any compact K$\"a$hler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K$\"a$hler-Einstein metric of general type. Moreover, we prove that, on a compact symplectic…

Let $X$ be a canonically polarized variety, i.e. a complex projective variety such that its canonical class $K_{X}$ defines an ample $\Q-$line bundle, and satisfying the conditions $G_1$ and $S_2$. Our main result says that $X$ admits a…

For a wide class of Dirichlet series associated to automorphic forms, we show that those without Euler products must have zeros within the region of absolute convergence. For instance, we prove that if f is a classical holomorphic modular…

Let $K$ be a bounded convex domain in $\mathbb{R}^2$ symmetric about the origin. The critical locus of $K$ is defined to be the (non-empty compact) set of lattices $\Lambda$ in $\mathbb{R}^2$ of smallest possible covolume such that $\Lambda…

Let $\pi: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact K\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique K\"ahler-Einstein…

We propose new types of canonical metrics on K\"ahler manifolds, called coupled K\"ahler-Einstein metrics, generalizing K\"ahler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and…

Several rigidity results are proved for critical points of natural Riemannian functionals on the space of metrics on 3-manifolds. Two of these results are as follows. Let (N, g) be a complete Riemannian 3-manifold, satisfying one of the…

We consider complete K\"ahler manifolds with nonnegative Ricci curvature. The main results are: 1. When the manifold has nonnegative bisectional curvature, we show that $\lim\limits_{r\to\infty}\frac{r^{2}}{vol(B(p, r))}\int_{B(p, r)}S$…

We prove that a product complex manifold cannot admit a complete K\"ahler metric with sectional curvature $K<c<0$ and Ricci curvature $Ric > d$, where $c$ and $d$ are constants. In particular, a product domain in $\C$ cannot cover a compact…

Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.

In this note, we look at estimates for the scalar curvature k of a Riemannian manifold M which are related to spin^c Dirac operators: We show that one may not enlarge a Kaehler metric with positive Ricci curvature without making k smaller…

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…

We give sufficient conditions for the existence of Kaehler-Einstein and constant scalar curvature Kaehler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kaehler classes and…