Related papers: Peak points for pseudoconvex domains: a survey

We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal domains, there exist at most finitely many non-congruent domains…

Given a pseudoconvex domain U with C^1-boundary in P^n, n>2, we show that if H^{2n-2}_\dR}(U)\not=0, then there is a strictly psh function in a neighborhood of boundary U. We also solve the \dbar-equation in X=P^n\ U, for data smooth (0,1)…

We study some properties of the coincidence set for the boundary Signorini problem, improving some results from previous works by the second author and collaborators. Among other new results, we show here that the convexity assumption on…

We discuss some extremal bases for $\CC$-convex domains.

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,…

Geometric lower and upper estimates are obtained for invariant metrics on $\Bbb C$-convex domains containing no complex lines.

We prove a variant of Rauch's hot spots conjecture for hyperbolic planar domains with small Neumann or mixed Dirichlet-Neumann eigenvalues. We conclude, for instance, that on bounded convex domains in the hyperbolic plane with sufficiently…

The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the…

This paper surveys results concerning peak sets and boundary interpolation sets for the unit disc. It includes hitherto unpublished results proved by David C. Ullrich on peak sets for the Zygmund class.

We prove that an open set $D$ in $\C^n$ is pseudoconvex if and only if for any $z\in D$ the largest balanced domain centered at $z$ and contained in $D$ is pseudoconvex, and consider analogues of that characterization in the linearly 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.

Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given.

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…

The second eigenfunction of the Neumann Laplacian on convex, planar domains is considered. Inspired by the famous hot spots conjecture and a related result of Steinerberger, we show that potential critical points of this eigenfunction (and,…

We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.

In this article, we prove a Lichnerowicz estimate for a compact convex domain of a K\"ahler manifold whose Ricci curvature satisfies $\Ric \ge k$ for some constant $k>0$. When equality is achieved, the boundary of the domain is totally…

A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of…

Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly…

We show that two smoothly bounded, strongly pseudoconvex domains which are diffeomorphic may be smoothly deformed into each other, with all intermediate domains being strongly pseudoconvex. This result relates to Lempert's ideas about…

A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.