Related papers: Extremal metrics on del Pezzo threefolds

We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our…

We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on \RCD\, metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These…

In this paper we study the supremum of Perelman's \lambda-functional {\lambda }_M(g) on Riemannian 4-manifold M by using the Seiberg-Witten equations. We prove among others that, for a compact K\"{a}hler-Einstein complex surface (M, J,…

We consider properly discontinuous, isometric, convex cocompact actions of surface groups on a CAT(-1) space. We show that the limit set of such an action, equipped with the canonical visual metric, is a (weak) quasicircle in the sense of…

We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least $5$. We also show that the same result is true for all odd-dimensional exotic spheres that bound…

We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type $\left\{k_i\times\frac{1}{r_i}(1,a_i): 3\le r_i \le 10,k_i \in \ZZ_{\ge 0}\right\}$; as well-formed and quasismooth varieties…

We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent…

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 prove that the twisted Kahler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when…

Let $(M,g)$ be an $n$-dimensional asymptotically flat Riemannian manifold with nonnegative scalar curvature that admits a noncompact area-minimizing hypersurface $\Sigma \subset M$. In the case where $n = 3$, O. Chodosh and the first-named…

The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a…

The present paper is composed of two parts. In the first one we define two pseudo-metrics $L_F$ and $K_F$ on the Teichmu\"uller space of semi-translation surfaces $\mathcal{TQ}_g(\underline k,\epsilon)$, which are the symmetric counterparts…

We prove that a complete K\"ahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete K\"ahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly…

Motivated by the study of Fano type varieties we define a new class of log pairs that we call asymptotically log Fano varieties and strongly asymptotically log Fano varieties. We study their properties in dimension two under an additional…

In Carnot groups of step 2 we consider sets having maximal or minimal possible homogeneous Hausdorff dimension compared to their Euclidean one: in the first case we prove that they must be in a sense vertical, that is a large part of these…

In this article, we derive estimates of Teichm\"uller modular forms, and associated invariants. Let $\mathcal{M}_{g}$ denote the moduli space of compact hyperbolic Riemann surfaces of genus $g\geq 2$, and let $\overline{M}_{g}$ be the…

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of…

An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose…

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar…

We develop a general theory for the existence of extremal K\"ahler metrics of Poincar\'e type in the sense of Auvray, defined on the complement of a toric divisor of a polarized toric variety. In the case when the divisor is smooth, we…