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Investigations in Hadamard spaces

dc.contributor.advisorLuke, Russell Prof. Dr.
dc.contributor.authorBërdëllima, Arian
dc.date.accessioned2021-08-27T09:28:52Z
dc.date.available2021-08-27T09:28:52Z
dc.date.issued2021-08-27
dc.identifier.urihttp://hdl.handle.net/21.11130/00-1735-0000-0008-58F4-2
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-8802
dc.description.abstractKjo tezë e doktoratës hulumton ndërveprimin midis gjeometrisë dhe analizës konvekse në hapësirat Hadamard. E motivuar nga aplikime të shumta të gjeometrisë CAT(0), puna jonë bazohet në rezultatet e shumë autorëve të mëparshëmnë mbi analizën konvekse dhe gjeometrinë në sensin e Alexandrovit. Hetimet tona u përgjigjen disa pyetjeve në teorinë e hapësirave CAT(0) prej të cilave disa janë parashtruar si probleme të hapura në literaturën e fundit. Teza jonë e doktoratës zhvillohet sipas linjave të mëposhtme: 1. Topologjitë e dobëta në hapësirat Hadamard, 2. Konveksifikimi i bashkësive kompakte, 3. Problemi i pemës mesatare në hapësirat e pemëve filogjenetike, 4. Konvergjenca Mosko në hapësirat Hadamard, 5. Operatorët (plotësisht) jo-ekspansivë dhe aplikimet e tyre në hapësirat Hadamard.de
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titleInvestigations in Hadamard spacesde
dc.typedoctoralThesisde
dc.contributor.refereeWardetzky, Max Prof. Dr.
dc.date.examination2020-08-27
dc.description.abstractgerDiese Doktorarbeit untersucht das Zusammenspiel zwischen Geometrie und konvexer Analyse in Hadamardräumen. Motiviert durch zahlreiche Anwendungen der CAT(0)-Geometrie baut unsere Arbeit auf den Ergebnissen vieler früherer Autoren in der konvexen Analysis und der Alexandrov-Geometrie auf. Unsere Untersuchungen beantworten mehrere Fragen in der Theorie von CAT(0)-Räumen, von denen einige in der neueren Literatur als offene Probleme gestellt wurden. Zusammengefasst entwickelt sich unsere Dissertation in folgende Richtungen: 1. Schwache Topologien in Hadamard-Räumen, 2. Konvexe Hüllen kompakter Mengen, 3. Mittleres Baumproblem in phylogenetischen Baumräumen, 4. Mosco-Konvergenz in Hadamard-Räumen, 5. Fest nichtexpansive Operatoren und ihre Anwendungen in Hadamard-Räumen.de
dc.description.abstractengThis thesis investigates the interplay between geometry and convex analysis in Hadamard spaces. Motivated by numerous applications of CAT(0) geometry, our work builds upon the results in convex analysis and Alexandrov geometry of many previous authors. Our investigations answer several questions in the theory of CAT(0) spaces some of which were posed as open problems in recent literature. In a nutshell our thesis develops along the following lines: 1. Weak topologies in Hadamard spaces, 2. Convex hulls of compact sets, 3. Mean tree problem in phylogenetic tree spaces, 4. Mosco convergence in Hadamard spaces, 5. Firmly nonexpansive operators and their applications in Hadamard spaces.de
dc.contributor.coRefereeHuckemann, Stephan Prof. Dr.
dc.contributor.thirdRefereeSchick, Thomas Prof. Dr.
dc.subject.gerHadamard spacede
dc.subject.gergeodesicsde
dc.subject.gernonpositive curvaturede
dc.subject.gerweak topologyde
dc.subject.gerweak convergencede
dc.subject.gergeodesically monotonede
dc.subject.gerconvex hullsde
dc.subject.gerphylogenetic treesde
dc.subject.gerFréchet meande
dc.subject.gerthreadingde
dc.subject.gerthreading degreede
dc.subject.gerMosco convergencede
dc.subject.gerproximal mappingsde
dc.subject.gerfirmly nonexpansive operatorsde
dc.subject.gerconvex combinations of operatorsde
dc.subject.gercompositions of operatorsde
dc.subject.germetric subregularityde
dc.subject.engHadamard spacede
dc.subject.enggeodesicsde
dc.subject.engnonpositive curvaturede
dc.subject.engweak topologyde
dc.subject.engweak convergencede
dc.subject.enggeodesically monotonede
dc.subject.engconvex hullsde
dc.subject.engphylogenetic treesde
dc.subject.engFréchet meande
dc.subject.engthreadingde
dc.subject.engthreading degreede
dc.subject.engMosco convergencede
dc.subject.engproximal mappingsde
dc.subject.engfirmly nonexpansive operatorsde
dc.subject.engconvex combinations of operatorsde
dc.subject.engcompositions of operatorsde
dc.subject.engmetric subregularityde
dc.identifier.urnurn:nbn:de:gbv:7-21.11130/00-1735-0000-0008-58F4-2-2
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn1768022348


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