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Über die Eigenschaften von K. Beretskys Partitionskonstruktionen

Über die Eigenschaften von K. Beretskys Partitionskonstruktionen

Vladimir BALKAN

51,12 €
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Editorial:
KS OmniScriptum Publishing
Año de edición:
2023
Materia
Geometría
ISBN:
9786206983729
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Dieses Buch ist einer Übersicht über nicht-normale Partitionen des hyperbolischen Raums gewidmet, insbesondere einer Übersicht über unregelmäßige Partitionen von K. Beretsky und einigen nützlichen Konsequenzen der vorgeschlagenen Konstruktionen. Mit Hilfe dieser Partition (Beretsky’s) ist es einfach, Beispiele für nicht-normale Partitionen des n-dimensionalen hyperbolischen Raums zu konstruieren (konstruktiver Beweis des Existenzsatzes) durch gleiche kompakte konvexe Polyeder, und diese Partitionen können nicht in reguläre Partitionen umgewandelt werden, indem man die Partitionspolyeder transponiert. In dieser Arbeit werden einige mögliche Verallgemeinerungen der Konstruktion von K. Beretsky aufgezeigt, die in den meisten Fällen auch die Konstruktion von nicht-normalen Partitionen erlauben. Die Besonderheiten der Partitionen erlauben es, einige allgemeine Aussagen, z.B. über Delaunay-Punktsysteme und Delaunay-Partitionen, konstruktiv zu beweisen. In der Veröffentlichung wird auch die Frage nach der Anzahl der Hyperfacetten einer (hyperbolischen) Krawatte erörtert.

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