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Wednesday, May 20, 2020 | History

2 edition of Holomorphic maps between convex domains in C r found in the catalog.

Holomorphic maps between convex domains in C r

Peter R. Mercer

# Holomorphic maps between convex domains in C r

## by Peter R. Mercer

Written in English

Edition Notes

Thesis (Ph.D.)--University of Toronto, 1992.

 ID Numbers Statement Peter R. Mercer. Open Library OL20743028M

COMPLEX GEOMETRY OF CONVEX DOMAINS THAT COVER VARIETIES This technique has many applications; to boundary regularity of holomorphic maps, to non-convexity of embeddings of Teichmtiller spaces in C", to classifying automorphism group actions on domains, to constructing canonical embeddings ofFile Size: 1MB. A proof of convex domains are domains of holomorphy. Ask Question Asked 3 years, 8 months ago. If you can find a zero set of a holomorphic function defined on a larger domain which touches your boundary, then that's a point through with you cannot extend. Thanks for contributing an answer to Mathematics Stack Exchange!

In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one infinite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Author: Taishun Liu, Xiaomin Tang, Jianfei Wang. Random holomorphic iteration in convex domains Example Let {g j} be any sequence of holomorphic self maps of D whose associated holomorphic iterated function system has some non-constant limit g and whose image is contained in some set X ⊂ D. Let us deﬁne f j: Bn → Bn by f.

arXivv1 [] 28 Dec Horoballs and iteration of holomorphic maps on bounded symmetric domains Cho-Ho Chua,∗, Michael Rigbyb a School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK b School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK Abstract. Given a ﬁxed-point free compact holomorphic self-map f on a. Lemma Let D b Cn be bounded domain and b ∈ @D be a local peak point of D. Suppose {Fi} is a sequence of holomorphic maps from a domain U ⊂ Ck into D and there is a point z0 ∈ U such that Fi(z0) → b as i → ∞. Then Fi(z) → b uniformly on every compact subset of U. We need another lemma which is proven in [7] using Fatou’s theorem on the.

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### Holomorphic maps between convex domains in C r by Peter R. Mercer Download PDF EPUB FB2

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is, at every point of its domain, complex differentiable in a neighborhood of the point.

The existence of a complex derivative in a neighbourhood is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal, locally, to its own. COMPLEX GEODESICS AND ITERATES OF HOLOMORPHIC MAPS ON CONVEX DOMAINS IN C PETER R.

MERCER Abstract. We study complex geodesies /: A —> fi, where A is the unit disk in C and ii belongs to a class of bounded convex domains in C with no boundary regularity assumption.

Along with continuity up to the boundary. Cite this article. Dini, G., Selvaggi Primicerio, A. Proper holomorphic maps between Reinhardt domains and strictly pseudoconvex domains. by: 1. Abstract. We consider two problems for holomorphic maps into convex domains in ℂ first is to give conditions under which a holomorphic map which is an isometry for the infinitesimal Kobayashi metric at one point must be by: 1.

A localization principle for biholomorphic mappings between the Fock-Bargmann-Hartogs domains Kodama, Akio, Hiroshima Mathematical Journal, ; A Local extension of proper holomorphic maps between some unbounded domains in \${\mathbb C}^n\$ Ayed, Besma and Ourimi, Nabil, Bulletin of the Belgian Mathematical Society - Simon Stevin, Transversality of holomorphic mappings between Cited by: 2.

BETWEEN CONVEX DOMAINS IN C" PETER R. MERCER (Communicated by Clifford J. Earle, Jr.) Abstract. We use a general version of the well-known Hopf lemma to study boundary regularity of proper holomorphic mappings between some bounded convex domains in C which carry no boundary regularity assumption.

Introduction Let Qx and Q2 be domains in C. isometries (thus proper holomorphic maps) from Bn to DIV m if n+ 2 ≤ m≤ 2n+ 2. Section 5 is devoted to establishing degree estimates for holomorphic isometric maps from Bn to DIV m.

In Section 6, we construct non-totally geodesic proper holomorphic maps from Bn to Ω where Ω is any of the four types of classical domains. ADVANCES IN MATHEMAT () Iterates of Holomorphic and kD-Nonexpansive Mappings in Convex Domains in C" TADEUSZ KUCZUMOW AND ADAM STACHURA Instytut Matematyki UMCS, Plac Marii Curie-Sklodowskiej 1, Lublin, Poland INTRODUCTION Throughout this paper D will be a bounded domain in C" and kD will be its Kobayashi by: If, a non-degenerate holomorphic mapping is a conformala non-degenerate holomorphic mapping does not, in general, preserve angles between a holomorphic mapping is non-degenerate at a point and if, then is locally invertible, i.e., then there exist neighbourhoods, and a holomorphic mapping such that for a holomorphic mapping maps onto in a one-to-one.

PROPER HOLOMORPHIC MAPS BETWEEN BOUNDED SYMMETRIC DOMAINS REVISITED GAUTAM BHARALI AND JAIKRISHNAN JANARDHANAN Abstract. We prove that a proper holomorphic map between two non-planar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomor-phism.

2, between bounded symmetric domains 1; 2. The pioneer works are due to Poincar e [P] and later to Alexander [Al] when 1; 2 are complex unit balls. In particular, any proper holomorphic self-map of the unit ball in Cn is an automorphism if n 2 [Al].

It is well-known that the rigidity properties fail dramatically for proper holomorphic maps betweenFile Size: KB. We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in \$\mathbb{C}^{n+1}\$. It appears, in particular, that it is controlled only by the first domain.

A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex Author: David E. Barrett.

In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a set which is maximal in the sense that there exists a holomorphic function on this set which cannot be extended to a bigger set.

Formally, an open set in the n-dimensional complex space is called a domain of holomorphy if there do not exist non-empty open sets ⊂ and ⊂ where is connected. Complexity of holomorphic maps from the complex unit ball to classical domains Ming Xiao and Yuan Yuan Abstract We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains.

We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. Approximation of holomorphic mappings on strongly pseudoconvex domains whose ﬁber enjoys the Convex Approximation Property (Theorem ).

Mathematics Subject Classiﬁcation: 32E10, 32E30, 32H02, 46G20, 58B For approximation of holomorphic maps from planar Jordan domains to. Holomorphic map synonyms, Holomorphic map pronunciation, Holomorphic map translation, English dictionary definition of Holomorphic map. Mathematics A function on a region of a complex plane, differentiable at every point in the region.

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable.

It then continues with a comprehensive introduction to integral. domains in n dimensional complex Euclidean space C" in such a way that the objects attached to holomorphically equivalent domains are identical.

If one succeeds in doing that, the objects thus associated with the domains are called (holomorphic) invariants of the domains. That domains have nontrivial invariants was first pointed out by Poincare. Special Toeplitz operators on strongly pseudoconvex domains McNeal, Jeffery D.

and Čučković, Željko, Revista Matemática Iberoamericana, ; Condition R and holomorphic mappings of domains with generic corners Chakrabarti, Debraj and Verma, Kaushal, Illinois Journal of Mathematics, ; Remark on Proper Holomorphic Maps Between Reducible Bounded Symmetric Domains Seo, Aeryeong Cited by: 9.

Electronic version of a print book. Innes, M. (). Understanding social control. Deviance, crime and social order. Berkshire, England: McGraw-Hill Education. Retrieved from Ebrary Academic Complete database. Dissertation from a database. Mercer, P.

R. (). Holomorphic maps between convex domains in C(n) (Doctoral dissertation). Retrieved Author: Kevin Harden.Suppose that Ω 1 and Ω 2 are two domains (not necessarily bounded) in C n and that f is a proper holomorphic mapping of Ω 1 onto Ω 2 of order r.

Let u = det [ f ′ ] and let F 1, F 2, ⋯, F r denote the r local inverses to f defined locally on Ω 2 ∖ S where S = { f (z): u (z) = 0 }.Cited by: Chapter 17 ety V C B, such that B\ V and A \f-1 (V) are complex manifolds and the restriction f: A \f-1 (V) + B\ V is a finitely sheeted holomorphic covering projection.

In this survey we shall consider proper holomorphic mappings f: D + D' between bounded domains DCC en and D' CC eN. Such mappings.