variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima...

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

inequality Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF). www.stat...

subharmonic function looks like a kind of convex function, so it was named by Levi as a pseudoconvex domain (Hartogs's pseudoconvexity). Pseudoconvex domain...

quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense...

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

theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets...

leads to the notion of pseudoconvexity. Cauchy–Riemann equations Holomorphic function Paley–Wiener theorem Quasi-analytic function Infinite compositions...

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

method Convex analysis — function f such that f(tx + (1 − t)y) ≥ tf(x) + (1 − t)f(y) for t ∈ [0,1] Pseudoconvex function — function f such that ∇f · (y −...

and only if it is (strictly) pseudoconvex as a CR manifold from the side of the domain. (See plurisubharmonic functions and Stein manifold.) An abstract...

strongly pseudoconvex manifold. The latter means that it has a strongly pseudoconvex (or plurisubharmonic) exhaustive function, i.e. a smooth real function ψ...

and the plurisubharmonic functions. Geometrically, these classes of functions correspond to convex domains and pseudoconvex domains, but there are also...

problem. Behnke–Stein theorem Levi pseudoconvex solution of the Levi problem Stein manifold Steven G. Krantz. Function Theory of Several Complex Variables...

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...

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

property than quasiconvexity. A linear-fractional objective function is both pseudoconvex and pseudoconcave, hence pseudolinear. Since an LFP can be transformed...

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

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

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

a special case. In the theory of functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the...

Diederich K, Fornaess JE (1975). "Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains". Proc Natl Acad Sci U S A. 72 (9): 3279–3280...

\Omega } . The decomposition in the theorem is feasible also on many non-pseudoconvex domains. The proof of the theorem follows from Hefer's lemma. Let Ω ⊂...

the distance to the boundary. This property shows that the domain is pseudoconvex. Historically, this lemma was first shown in the Hartogs domain in the...

complex manifold Complex manifold Kähler manifold Pluriharmonic function Pseudoconvexity Rizza manifold Several complex variables The detailed motivation...

of Mathematics (2000) Hirachi constructed CR invariants of strongly pseudoconvex boundaries via a deep study of the logarithmic singularity of the Bergman...

her Ph.D. in 1993. Her doctoral dissertation, Hardy Spaces on Strongly Pseudoconvex Domains in C n {\displaystyle C^{n}} and Domains of Finite Type in C...

Epstein, R B Melrose, G A Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains. Acta Mathematica 167 (1991), no. 1–2, 1–106. C L Epstein, The...

regularity in the sense of preservation of Sobolev spaces on large class of pseudoconvex domains. Boas also provided a counterexample to the Lu Qi-Keng Conjecture...

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