Analytic Set-Valued Functions and Spectra.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
A generalization of Vesentini and Wermer's theorems
On ideals consisting of joint topological divisors of zero
An open mapping theorem for analytic multifunctions
The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.
An infinite family of joint spectra
A criterion for subharmonicity of a function of the spectrum
Polynomially convex hulls of families of arcs
The paper is devoted to the study of polynomially convex hulls of compact subsets of ℂ², fibered over the boundary of the unit disc, such that all fibers are simple arcs in the plane and their endpoints form boundaries of two closed, not intersecting analytic discs. The principal question concerned is under what additional condition such a hull is a bordered topological hypersurface and, in particular, is foliated by a unique holomorphic motion. One of the main results asserts that this happens...
Extensions of holomorphic motions
The Bremermann-Dirichlet problem for -plurisubharmonic functions
Polynomial hulls in and quasicircles
Uniform algebras and analytic multifunctions
Dati due elementi e in un'algebra uniforme , sia . Nella presente Nota si danno, fra l’altro, due nuove dimostrazioni elementari del fatto che la funzione è subarmonica su e che l’applicazione è analitica nel senso di Oka.
Uniform algebras and analytic multifunctions
Dati due elementi e in un'algebra uniforme , sia . Nella presente Nota si danno, fra l’altro, due nuove dimostrazioni elementari del fatto che la funzione è subarmonica su e che l’applicazione è analitica nel senso di Oka.
Evolution of subsets of and parabolic problem for the Levi equation
Levi equation and evolution of subsets of
In this Note we state some results obtained studying the evolution of compact subsets of by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.
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