Related papers: On different extremal bases for $\CC$-convex domai…

In this paper after extending the definition of symplectic duality (given by the first two authors in arXiv:math/0603141 for bounded symmetric domains) to arbitrary complex domains of ${\C}^n$ centered at the origin we generalize some of…

In this paper we introduce and study the concept of set extremality for systems of convex sets in vector spaces without topological structures. Characterizations of the extremal systems of sets are obtained in the form of the convex…

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.

This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been published elsewhere.

We establish a new $W^{1,2\frac{n-1}{n-2}}$ estimate for the extremal solution of $-\Delta u=\lambda f(u)$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^n$, which is convex, for arbitrary positive and increasing nonlinearities $f\in…

We present some results in the analysis of non-compact differential equations on unbounded domains.

In this present paper, we solve the $\partial\bar{\partial}$ for extendable currents definite in a pseudoconvexe unbounded domain of $\mathbb{C}^n$ .

Motivated by applications in materials science, a set of quasiconvexity at the boundary conditions is introduced for domains that are locally diffeomorphic to cones. These conditions are shown to be necessary for strong local minimisers in…

We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.

We treat the boundary problem for complex varieties (with isolated singularities) of dimension greater than one, which are contained in a suitable class of strictly pseudoconvex, unbounded domains of C^n.

We study extremal discs for the Kobayashi metric. Inspired by work of Lempert on strongly convex domains, we present results on strongly pseudoconvex domains. We also consider a useful biholomorphic invariant, inspired by the Kobayashi (and…

We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain,…

We discuss solutions of several questions concerning the geometry of conformal planes.

We give some detailed numerical information about extremal metrics on four different toric surfaces. These are sample of many other cases which can be treated using a computer programme outlined in the paper.

We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…

In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of $\mathbb{C}^2$, it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the…

Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…