function. In one complex dimension, every open domain is pseudoconvex. The concept of pseudoconvexity is thus more useful in dimensions higher than 1. Analytic...

it was named by Levi as a pseudoconvex domain (Hartogs's pseudoconvexity). Pseudoconvex domain (boundary of pseudoconvexity) are important, as they allow...

of η {\displaystyle \eta } -pseudoconvexity and η {\displaystyle \eta } -pseudolinearity; wherein classical pseudoconvexity and pseudolinearity pertain...

depend on the pseudoconvexity. This nomenclature comes from the study of pseudoconvex domains: M is the boundary of a (strictly) pseudoconvex domain in C...

The characterization of domains of holomorphy leads to the notion of pseudoconvexity. Cauchy–Riemann equations Holomorphic function Paley–Wiener theorem...

Logarithmically concave function Pseudoconvexity in the sense of several complex variables (not generalized convexity) Pseudoconvex function Invex function Concavification...

to study smooth but not holomorphic functions, see for example Levi pseudoconvexity. When dealing with holomorphic functions, we could consider the Hessian...

functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the domain of existence of such functions:...

theorem Holomorphically convex hull Integrally-convex set John ellipsoid Pseudoconvexity Radon's theorem Shapley–Folkman lemma Symmetric set Morris, Carla C...

monotone property, pseudoconvexity, which is a stronger property than quasiconvexity. A linear-fractional objective function is both pseudoconvex and pseudoconcave...

study of the asymptotics of the Bergman kernel off the boundaries of pseudoconvex domains in C n {\displaystyle \mathbb {C} ^{n}} . He has studied mathematical...

notions are intermediate between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André...

metrics of negative scalar curvature on any bounded, smooth, and strictly pseudoconvex subset of complex Euclidean space.[CY80] These can be thought of as complex...

Northwestern University University of California, Berkeley Thesis A priori pseudoconvexity energy estimates in domains with boundary and applications to exact...

-holomorphic function defined on a bounded Stein manifold (such as a pseudoconvex compact set in C n {\displaystyle \mathbb {C} ^{n}} of dimension less...

(1954), doi:10.4099/jjm1924.23.0_97, MR 0071089 Siu, Yum-Tong (1978), "Pseudoconvexity and the problem of Levi", Bulletin of the American Mathematical Society...

surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum. This is in...

the derivative Karamata's inequality Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture...

{\displaystyle {\bar {\partial }}} -Poincaré lemma holds in more generality for pseudoconvex domains. Using both the Poincaré lemma and the ∂ ¯ {\displaystyle {\bar...

equivalent to being a (complex) strongly pseudoconvex manifold. The latter means that it has a strongly pseudoconvex (or plurisubharmonic) exhaustive function...

several complex variables, plurisubharmonic functions are used to describe pseudoconvex domains, domains of holomorphy and Stein manifolds. The main geometric...

University of Washington under Edgar Lee Stout with thesis Embedding Strictly Pseudoconvex Domains in Convex Domains. At Princeton University he became in 1974...

Kohn with thesis Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains. He is a professor at Purdue University. He solved a boundary...

III], Kuranishi developed the theory of harmonic integrals on strongly pseudoconvex CR structures over small balls along the line developed by D. C. Spencer...

of type I functions introduced by Rueda and Hanson. Convex function Pseudoconvex function Quasiconvex function Hanson, Morgan A. (1981). "On sufficiency...

algebraic surfaces Mirror symmetry Multiplier ideal Projective variety Pseudoconvexity Several complex variables Stein manifold Voisin, C., 2016. The Hodge...

q {\displaystyle i<{\rm {{codh}\;({\mathcal {F}})-q}}} ), if X is q-pseudoconvex (resp. q-pseudoconcave). (finiteness) H i ( X , F ) = 0 {\displaystyle...

Kohn, following earlier work by Kohn, studied the ∂-Neumann problem on pseudoconvex domains, and demonstrated the relation of the regularity theory to the...

doi:10.1007/s13226-018-0267-6. S2CID 119147594. Peternell, Th. (1994). "Pseudoconvexity, the Levi Problem and Vanishing Theorems". Several Complex Variables...

This is related to the fact that an increasing union of pseudoconvex domains is pseudoconvex and so it can be proven using that fact and the solution...