Pluripotential TheoryPluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two concepts provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. A substantial proportion of the work is devoted to classical properties of subharmonic and plurisubharmonic functions, which makes the pluripotential theory available for the first time to a wide audience of analysts. |
Contents
Complex differentiation | 3 |
Subharmonic and plurisubharmonic functions | 20 |
Exercises | 81 |
6 other sections not shown
Common terms and phrases
Bedford and Taylor biholomorphic C-linear C²(N Cegrell Co(N compact open subset compact set compact subset complex variable Consequently continuous converges convex functions Corollary dd°u dd°v decreasing sequence Define Demailly denote Dirichlet problem estimate exists ƏzjƏžk formula func gn(z harmonic functions hence holomorphic functions holomorphic mapping hyperconvex implies K₁ Klimek L-regular Lebesgue Lebesgue measure Lemma Let f lim sup locally bounded locally uniformly maximal maximum principle measure Monge-Ampère operator Moreover neighbourhood non-negative open set open subset pluricomplex Green function pluriharmonic pluripolar sets plurisubharmonic functions polynomially convex positive Proof Let properties Proposition prove pseudoconvex PSH(C PSH(N relatively compact open result satisfies SH(N Siciak subharmonic functions submanifold subset of Rm Suppose topology u₁ upper semicontinuous
References to this book
Invariant Distances and Metrics in Complex Analysis Marek Jarnicki,Peter Pflug No preview available - 1993 |