Related papers: A note on higher extremal metrics

We study the Dirichlet problem of the Abreu equation. The solutions provide the Kahler metrics of constant scalar curvature on the complex torus.

We show that the blowup of an extremal Kahler manifold at a relatively stable point in the sense of GIT admits an extremal metric in Kahler classes that make the exceptional divisor sufficiently small, extending a result of…

In this paper, we derive apriori estimates for constant scalar curvature K\"ahler metrics on a compact K\"ahler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the K\"ahler potential. We also…

Let (X,\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\"ahler class \Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative…

We consider constant scalar curvature K\"{a}hler metrics on a smooth minimal model of general type in a neighborhood of the canonical class, which is the perturbation of the canonical class by a fixed K\"{a}hler metric. We show that…

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

Geometric (also known as spatial) quantiles, introduced by Chaudhury and representing one of the three principal approaches to defining multivariate quantiles, have been well studied in the literature. In this work, we focus on the extremal…

The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact $4-$dimensional manifold $(M^4,g_0)$ with positive scalar curvature. We prove new exitence criterium which provides existence…

A set of recent results indicates that fractionally filled bands of Chern insulators in two dimensions support fractional quantum Hall states analogous to those found in fractionally filled Landau levels. We provide an understanding of…

The stability of fractional Chern insulators is widely believed to be predicted by the resemblance of their single-particle spectra to Landau levels. We investigate the scope of this geometric stability hypothesis by analyzing the stability…

In this paper, we investigate a Kazdan-Warner problem on compact K\"ahler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact K\"ahler surfaces when the…

The present paper concerns the question of the violation of the r-th inequality for extremal curves in the projective r-space, posed by T. Kato and G. Martens. We show that the answer is negative in many cases. The result is obtained by a…

We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying…

We give a survey of our recent work describing a method which combines the Sasaki join construction with the admissible K\"ahler construction of to obtain new extremal and new constant scalar curvature Sasaki metrics, including…

When studying the weighted Hardy-Rellich inequality in $L^2$ with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new…

In this article, we establish the existence of an extremal function for the k-th order critical Hardy-Sobolev-Maz'ya (HSM) inequalities on the upper half space $\mathbb{R}^{n+1}_{+}$ when $k\ge 2$ and $n\geq 2k+2$:…

We prove estimates for the sectional curvature of hyperkaehler quotients and give applications to moduli spaces of solutions to Nahm's equations and Hitchin's equations.

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove…

We investigate the interaction between quantum anomalous Hall (QAH) phases hosted by two atomically thin hexagonal lattices and demonstrate the emergence of topological phases with large Chern numbers. Interlayer coupling between two…