Related papers: A remark on the relative extremal function

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive…

Summability has been a central object of study in difference algebra over the past half-century. It serves as a cornerstone of algebraic methods to study linear recurrences over various fields of coefficients and with respect to various…

We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…

We generalize the bifurcation technique of Bando-Mabuchi in the context of extremal metrics.

We give geometrical conditions under which there exist extremal functions for the sharp $L^2$-Nash inequality.

Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f…

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is…

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…

In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…

We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.

For linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, we study functional convergence of the joint partial sum and partial maxima processes. We derive a…

This paper focus on the symmetry and symmetry breaking about the second order Hydrogen Uncertainty Principle. \emph{Firstly}, by choosing a suitable test function, we give a negative answer to the conjecture presented by Cazacu, Flynn and…

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

In this paper we consider an extremal problem in geometry. Let $\lambda$ be a real number and $A$, $B$ and $C$ be arbitrary points on the unit circle $\Gamma$. We give full characterization of the extremal behavior of the function…

We prove a result on the relationship between the relative conormal space of an analytic function $f$ on affine space and the relative conormal space of $f$ restricted to a hyperplane slice, at a point where the relative conormal space of…

Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…

We show that if a compact K\"ahler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises…