Complex convexity

Definition

A set Ω in $\mathbb{C}^n$ is called $\mathbb{C}$-convex if its intersection with any complex line is contractible.

Background

In complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function behavior. Examples of classes of functions with a rich structure are, in addition to the convex functions, the subharmonic functions and the plurisubharmonic functions. Geometrically, these classes of functions correspond to convex domains and pseudoconvex domains, but there are also other types of domains, for instance lineally convex domains which can be generalized using convex analysis. A great deal is already known about these domains, but there remain some fascinating, unsolved problems. This theme is mainly theoretical, but there are computational aspects of the domains studied, and these computational aspects are certainly worthy of further study.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Complex analysis Convex analysis Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Jack's River Henryk Gulbinowicz Look at other dictionaries: Bond convexity — In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher …   Wikipedia Hardy space — In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G. H. Hardy, because of the… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia Convex set — A convex set …   Wikipedia Polygon — For other uses, see Polygon (disambiguation). Some polygons of different kinds In geometry a polygon (   …   Wikipedia Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… …   Wikipedia Riesz–Thorin theorem — In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem is a result about interpolation of operators. It is named after Marcel Riesz and his student G. Olof… …   Wikipedia John von Neumann — Von Neumann redirects here. For other uses, see Von Neumann (disambiguation). The native form of this personal name is Neumann János. This article uses the Western name order. John von Neumann …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”