Sökning: "holomorphic extension"

Hittade 5 avhandlingar innehållade orden holomorphic extension.

1. 1. Holomorphic embeddings and applications

   Författare :Sam Lodin; Frank Kutzschebauch; Jörgen Boo; Frank Wikström; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Anders´en-Lempert-theory; holomorphic embeddings; Eisenman hyperbolicity; holomorphic group actions; plurisubharmonic extension; analytic polyhedron; MATHEMATICS; MATEMATIK;

   Sammanfattning : In the first part of this thesis we consider the question of the number of equivalenceclasses of holomorphic embeddings of Ck into Cn. We show the existence of holomorphicfamilies of proper holomorphic embeddings of Ck into Cn (0 < k < n−1),such that members of the family are pairwise nonequivalent in a suitable sense. LÄS MER

3. 2. Holomorphic extension and schlichtness on tube manifolds

   Författare :Suprokash Hazra; Egmont Porten; Cornelia Schiebold; Andreas Lind; Per Åhag; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Envelopes of holomorphy; truncated tube domains; holomorphic extension; Bochner tube; manifold; schlichtness;

   Sammanfattning : We first investigate the holomorphic extension of some classical and accessible classes of domains in $\mathbb{C}^n$ to know to what extent their envelopes are constructive. We give alternative proofs to some of the classical theorems using only first-principle arguments and without involving higher Stein geometry. LÄS MER

4. 3. Positive vector bundles in complex and convex geometry

   Författare :Hossein Raufi; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Nakano positivity; vanishing theorems; Prekopa theorem; Griffiths positivity; convex geometry; Ohsawa-Takegoshi extension theorem; dbar-equation; L^2-estimates; singular hermitian metrics; holomorphic vector bundles; holomorphic vector bundles; dbar-equation; L^2-estimates; singular hermitian metrics; Griffiths positivity; Nakano positivity; vanishing theorems; Ohsawa-Takegoshi extension theorem; convex geometry; Prekopa theorem;

   Sammanfattning : This thesis concerns various aspects of the geometry of holomorphic vector bundles and their analytical theory which all, vaguely speaking, are related to the notion of positive curvature in general, and L^2-methods for the dbar-equation in particular. The thesis contains four papers. LÄS MER

5. 4. Regularity and uniqueness-related properties of solutions with respect to locally integrable structures

   Författare :Abtin Daghighi; Egmont Porten; Christer Kiselman; Stefan Borell; Jürgen Leiterer; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Maximum principle; hypocomplexity; locally integrable structure; hypoanalytic structure; weak pseudoconcavity; uniqueness; CR functions;

   Sammanfattning : We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. LÄS MER

7. 5. The Maximum Principle for Cauchy-Riemann Functions and Hypocomplexity

   Författare :Abtin Daghighi; Stefan Borell; Christer Kiselman; Egmont Porten; Juergen Leiterer; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Hypocomplexity; hypoanalytic structure; CR functions; maximum principle; weak pseudoconcavity;

   Sammanfattning : This licentiate thesis contains results on the maximum principle forCauchy–Riemann functions (CR functions) on weakly 1-concave CRmanifolds and hypocomplexity of locally integrable structures. Themaximum principle does not hold true in general for smooth CR functions,and basic counterexamples can be constructed in the presenceof strictly pseudoconvex points. LÄS MER