{"id":{"repo_id":"oldenburg","oai_identifier":"oai:oops.uni-oldenburg.de:245"},"canonical_url":"https://search.dev.ndltd.org/etd/oldenburg/oai:oops.uni-oldenburg.de:245","repository":{"repo_id":"oldenburg","name":"Carl von Ossietzky Universität Oldenburg","base_url":"http://oops.uni-oldenburg.de/cgi/oai2"},"display":{"title":"Tautness and Kobayashi hyperbolicity","abstract":"The main objects studied in this work are hyperbolicity, tautness, and completeness for domains in C n. In the first chapter we introduce necessary notions and facts. In particular, in §1.1 we give some properties related to the Minkowski functions. In §1.3 and §1.4 we recall Royden's criterion for taut domains. Applying it we give new proofs for some known results. We also present a motivation to study k-hyperbolicity. The second chapter is devoted to studying the hyperbolic (mainly k -, k -, Brody hyperbolic) Hartogs type domains. In §2.1 we give a full characterization of k-hyperbolicity for a class of Hartogs domain with balanced fibers. Moreover, we find some sufficient conditions for a Hartogs domain with balanced fibers to be k-hyperbolic. In §2.2 we discuss conditions for a Hartogs-Laurent domain to be hyperbolic. We also prove that for any n > 4 there is a Hartogs-Laurent domain in C n which has a local plurisubharmonic antipeak function at infinity, but which does not have a local plurisubharmonic peak function at infinity. The main goal of the third chapter is to study some new applications of Royden's criterion. In particular, we find a full characerization of tautness for the class of Hartogs type domains with balanced fibers. Moreover, a new relationship between (global) tautness and local tautness is established, which may be considered as a generalization of the Kerzmann-Rosay Theorem. In §3.4 and §3.5 we study hyperconvexity and k-completeness of some Hartogs type domains. The last chapter contains results on k-hyperbolicity and k-completeness for the class of balanced domains. In §4.1 we point out that there is a big difference between k-hyperbolicity and Brody hyperbolicity in the class of balanced domains. We prove that for any n > 3 there is a pseudoconvex non-k-hyperbolic balanced domain in C n with positive-definite Minkowski function that is Brody hyperbolic. In §4.2 we give another example of the following result obtained by Jarnicki-Pflug: For n > 3 there is a bounded pseudoconvex balanced domain in C n with continuous Minkowski function that is not k-complete.","abstract_html":"The main objects studied in this work are hyperbolicity, tautness, and completeness for domains in C n. In the first chapter we introduce necessary notions and facts. In particular, in §1.1 we give some properties related to the Minkowski functions. In §1.3 and §1.4 we recall Royden's criterion for taut domains. Applying it we give new proofs for some known results. We also present a motivation to study k-hyperbolicity. The second chapter is devoted to studying the hyperbolic (mainly k -, k -, Brody hyperbolic) Hartogs type domains. In §2.1 we give a full characterization of k-hyperbolicity for a class of Hartogs domain with balanced fibers. Moreover, we find some sufficient conditions for a Hartogs domain with balanced fibers to be k-hyperbolic. In §2.2 we discuss conditions for a Hartogs-Laurent domain to be hyperbolic. We also prove that for any n > 4 there is a Hartogs-Laurent domain in C n which has a local plurisubharmonic antipeak function at infinity, but which does not have a local plurisubharmonic peak function at infinity. The main goal of the third chapter is to study some new applications of Royden's criterion. In particular, we find a full characerization of tautness for the class of Hartogs type domains with balanced fibers. Moreover, a new relationship between (global) tautness and local tautness is established, which may be considered as a generalization of the Kerzmann-Rosay Theorem. In §3.4 and §3.5 we study hyperconvexity and k-completeness of some Hartogs type domains. The last chapter contains results on k-hyperbolicity and k-completeness for the class of balanced domains. In §4.1 we point out that there is a big difference between k-hyperbolicity and Brody hyperbolicity in the class of balanced domains. We prove that for any n > 3 there is a pseudoconvex non-k-hyperbolic balanced domain in C n with positive-definite Minkowski function that is Brody hyperbolic. In §4.2 we give another example of the following result obtained by Jarnicki-Pflug: For n > 3 there is a bounded pseudoconvex balanced domain in C n with continuous Minkowski function that is not k-complete.","abstract_has_math":false,"creators":["Park, Sung Hee"],"institution":"Universität Oldenburg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-02-12","date_published":"2003-02-12","updated_at":"2026-07-27T20:27:18Z","subjects":["[Keine Schlagwörter von Autor/in vergeben.]"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://oops.uni-oldenburg.de/245","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Park, Sung Hee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["BIS der Universität Oldenburg"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Oldenburg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["[Keine Schlagwörter von Autor/in vergeben.]"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The main objects studied in this work are hyperbolicity, tautness, and completeness for domains in C n. In the first chapter we introduce necessary notions and facts. In particular, in §1.1 we give some properties related to the Minkowski functions. In §1.3 and §1.4 we recall Royden's criterion for taut domains. Applying it we give new proofs for some known results. We also present a motivation to study k-hyperbolicity. The second chapter is devoted to studying the hyperbolic (mainly k -, k -, Brody hyperbolic) Hartogs type domains. In §2.1 we give a full characterization of k-hyperbolicity for a class of Hartogs domain with balanced fibers. Moreover, we find some sufficient conditions for a Hartogs domain with balanced fibers to be k-hyperbolic. In §2.2 we discuss conditions for a Hartogs-Laurent domain to be hyperbolic. We also prove that for any n > 4 there is a Hartogs-Laurent domain in C n which has a local plurisubharmonic antipeak function at infinity, but which does not have a local plurisubharmonic peak function at infinity. The main goal of the third chapter is to study some new applications of Royden's criterion. In particular, we find a full characerization of tautness for the class of Hartogs type domains with balanced fibers. Moreover, a new relationship between (global) tautness and local tautness is established, which may be considered as a generalization of the Kerzmann-Rosay Theorem. In §3.4 and §3.5 we study hyperconvexity and k-completeness of some Hartogs type domains. The last chapter contains results on k-hyperbolicity and k-completeness for the class of balanced domains. In §4.1 we point out that there is a big difference between k-hyperbolicity and Brody hyperbolicity in the class of balanced domains. We prove that for any n > 3 there is a pseudoconvex non-k-hyperbolic balanced domain in C n with positive-definite Minkowski function that is Brody hyperbolic. In §4.2 we give another example of the following result obtained by Jarnicki-Pflug: For n > 3 there is a bounded pseudoconvex balanced domain in C n with continuous Minkowski function that is not k-complete.","Die Hauptthemen, die in dieser Arbeit studiert werden, sind Hyperbolizität, Tautheit und Vollständigkeit für Gebiete im C n. Im ersten Kapitel führen wir die notwendigen Begriffe und Tatsachen ein. Insbesondere wiederholen wir in §1.1 Eigenschaften der Minkowski Funktion. In §1.3 und §1.4 erinnern wir an das Royden-Kriterium für Gebiete, die taut sind. Es anwendend geben wir neue Beweise für einige bekannte Resultate. Wir motivieren auch, warum die k-Hyperbolizität zu studieren ist. Das zweite Kapitel behandelt hyperbolische hauptsächlich k -, k -, Brody hyperbolische) Gebiete vom Hartogs Typ. In §2.1 geben wir eine volle Charakterisierung der k-Hyperbolizität für eine Klasse von Hartogs Gebieten mit vollkommen-zirkularen Fasern. Zudem finden wir hinreichende Bedingungen für ein Hartogs Gebiet mit vollkommen-zirkularen Fasern, k-hyperbolisch zu sein. In §2.2 besprechen wir Bedingungen, unter denen ein Hartogs-Laurent Gebiet hyperbolisch ist. Wir beweisen auch, daß für jedes n > 4 es ein Hartogs-Laurent Gebiet im C n gibt, das im Unendlichen eine lokale plurisubharmonische Antipeak-Funktion, aber keine plurisubharmonische Peak-Funktion hat. Das Hauptziel des dritten Kapitels ist es, einige neue Anwendungen des Royden-Kriteriums zu diskutieren. Insbesondere finden wir eine volle Charakterisierung für Hartogs Gebiete mit vollkommen-zirkularen Fasern, die taut sind. Außerdem wird eine neue Beziehung zwischen (globaler) Tautheit und lokaler Tautheit aufgestellt, die als Verallgemeinerung des Satzes von Kerzman-Rosay betrachtet werden kann. In §3.4 und §3.5 studieren wir die Hyperkonvexität und die k-Vollständigkeit von Gebieten vom Hartogs Typ. Das letzte Kapitel enthält Resultate für die k-Hyperbolizität und k-Vollständigkeit von vollkommen-zirkularen Gebieten. Wir unterstreichen in §4.1, daß es einen großen Unterschied zwischen k-Hyperbolizität und Brody-Hyperbolizität gibt. Wir beweisen, daß es für jedes n > 3 ein pseudokonvexes vollkommen-zirkulares Gebiet im C n mit positiv-definitiver Minkowski Funktion gibt, das Brody-hyperbolisch, aber nicht k-hyperbolisch ist. In §4.2 geben wir ein anderes Beispiel für folgendes Resultat von Jarnicki-Pflug: Für jedes n > 3 gibt es ein beschränktes pseudokonvexes vollkommen-zirkulares Gebiet im C n mit stetiger Minkowski Funktion, das nicht k-vollständig ist."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Tautness and Kobayashi hyperbolicity"]}]}],"canonical_facts":{"dc:creator":["Park, Sung Hee"],"dc:description.abstract":["The main objects studied in this work are hyperbolicity, tautness, and completeness for domains in C n. In the first chapter we introduce necessary notions and facts. In particular, in §1.1 we give some properties related to the Minkowski functions. In §1.3 and §1.4 we recall Royden's criterion for taut domains. Applying it we give new proofs for some known results. We also present a motivation to study k-hyperbolicity. The second chapter is devoted to studying the hyperbolic (mainly k -, k -, Brody hyperbolic) Hartogs type domains. In §2.1 we give a full characterization of k-hyperbolicity for a class of Hartogs domain with balanced fibers. Moreover, we find some sufficient conditions for a Hartogs domain with balanced fibers to be k-hyperbolic. In §2.2 we discuss conditions for a Hartogs-Laurent domain to be hyperbolic. We also prove that for any n > 4 there is a Hartogs-Laurent domain in C n which has a local plurisubharmonic antipeak function at infinity, but which does not have a local plurisubharmonic peak function at infinity. The main goal of the third chapter is to study some new applications of Royden's criterion. In particular, we find a full characerization of tautness for the class of Hartogs type domains with balanced fibers. Moreover, a new relationship between (global) tautness and local tautness is established, which may be considered as a generalization of the Kerzmann-Rosay Theorem. In §3.4 and §3.5 we study hyperconvexity and k-completeness of some Hartogs type domains. The last chapter contains results on k-hyperbolicity and k-completeness for the class of balanced domains. In §4.1 we point out that there is a big difference between k-hyperbolicity and Brody hyperbolicity in the class of balanced domains. We prove that for any n > 3 there is a pseudoconvex non-k-hyperbolic balanced domain in C n with positive-definite Minkowski function that is Brody hyperbolic. In §4.2 we give another example of the following result obtained by Jarnicki-Pflug: For n > 3 there is a bounded pseudoconvex balanced domain in C n with continuous Minkowski function that is not k-complete.","Die Hauptthemen, die in dieser Arbeit studiert werden, sind Hyperbolizität, Tautheit und Vollständigkeit für Gebiete im C n. Im ersten Kapitel führen wir die notwendigen Begriffe und Tatsachen ein. Insbesondere wiederholen wir in §1.1 Eigenschaften der Minkowski Funktion. In §1.3 und §1.4 erinnern wir an das Royden-Kriterium für Gebiete, die taut sind. Es anwendend geben wir neue Beweise für einige bekannte Resultate. Wir motivieren auch, warum die k-Hyperbolizität zu studieren ist. Das zweite Kapitel behandelt hyperbolische hauptsächlich k -, k -, Brody hyperbolische) Gebiete vom Hartogs Typ. In §2.1 geben wir eine volle Charakterisierung der k-Hyperbolizität für eine Klasse von Hartogs Gebieten mit vollkommen-zirkularen Fasern. Zudem finden wir hinreichende Bedingungen für ein Hartogs Gebiet mit vollkommen-zirkularen Fasern, k-hyperbolisch zu sein. In §2.2 besprechen wir Bedingungen, unter denen ein Hartogs-Laurent Gebiet hyperbolisch ist. Wir beweisen auch, daß für jedes n > 4 es ein Hartogs-Laurent Gebiet im C n gibt, das im Unendlichen eine lokale plurisubharmonische Antipeak-Funktion, aber keine plurisubharmonische Peak-Funktion hat. Das Hauptziel des dritten Kapitels ist es, einige neue Anwendungen des Royden-Kriteriums zu diskutieren. Insbesondere finden wir eine volle Charakterisierung für Hartogs Gebiete mit vollkommen-zirkularen Fasern, die taut sind. Außerdem wird eine neue Beziehung zwischen (globaler) Tautheit und lokaler Tautheit aufgestellt, die als Verallgemeinerung des Satzes von Kerzman-Rosay betrachtet werden kann. In §3.4 und §3.5 studieren wir die Hyperkonvexität und die k-Vollständigkeit von Gebieten vom Hartogs Typ. Das letzte Kapitel enthält Resultate für die k-Hyperbolizität und k-Vollständigkeit von vollkommen-zirkularen Gebieten. Wir unterstreichen in §4.1, daß es einen großen Unterschied zwischen k-Hyperbolizität und Brody-Hyperbolizität gibt. Wir beweisen, daß es für jedes n > 3 ein pseudokonvexes vollkommen-zirkulares Gebiet im C n mit positiv-definitiver Minkowski Funktion gibt, das Brody-hyperbolisch, aber nicht k-hyperbolisch ist. In §4.2 geben wir ein anderes Beispiel für folgendes Resultat von Jarnicki-Pflug: Für jedes n > 3 gibt es ein beschränktes pseudokonvexes vollkommen-zirkulares Gebiet im C n mit stetiger Minkowski Funktion, das nicht k-vollständig ist."],"dc:format.medium":["application/pdf"],"dc:publisher":["BIS der Universität Oldenburg"],"dc:subject":["[Keine Schlagwörter von Autor/in vergeben.]"],"dc:title":["Tautness and Kobayashi hyperbolicity"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Oldenburg"]},"updated_at":"2026-07-27T20:27:18Z"}