相关论文: Peak points for pseudoconvex domains: a survey

We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly $\ell_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago…

Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract…

An example is given of a hyperconvex manifold without non-constant bounded holomorphic functions, which is realized as a domain with real-analytic Levi-flat boundary in a projective surface.

We extend some theorems for the Infinity-Ground State and for the Infinity-Potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

Let $\Omega \subset \mathbb{R}^2$ be a bounded, convex domain and let $-\Delta \phi_1 = \mu_1 \phi_1$ be the first nontrivial Laplacian eigenfunction with Neumann boundary conditions. The Hot Spots conjecture claims that the maximum and…

In this paper, we investigate the asymptotic behavior of the Bergman kernel at the boundary for some pseudoconvex model domains. This behavior can be described by the geometrical information of the Newton polyhedron of the defining function…

We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…

We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.

In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a question raised by D. Barrett, this approach is formulated…

The latest results on searches for supersymmetry, extra dimensions and exotic phenomena from the LEP collaborations are presented. No significant signal-like excess is observed in the data. The results are interpreted in various models and…

This article shows the existence of a class of closed bounded matrix convex sets which do not have absolute extreme points. The sets we consider are noncommutative sets, $K_X$, formed by taking matrix convex combinations of a single tuple…

We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give…

This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.

We study the boundary behaviour of the Fefferman--Szeg\"o metric and several associated invariants in a $C^\infty$-smoothly bounded strictly pseudoconvex domain.

The hot spots conjecture asserts that for any convex bounded domain $\Omega$ in $\mathbb R^d$, the first non-trivial Neumann eigenfunction of the Laplace operator in $\Omega$ attains its maximum at the boundary. We construct counterexamples…

We show some lower estimates for the Kobayashi-Royden metric on a class of smooth bounded pseudoconvex domains.

Some recent existence, multiplicity, and uniqueness results for singular p-Laplacian systems either in bounded domains or in the whole space are presented, with a special attention to the case of convective reactions. A extensive…

We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and…