02883nam 22005415 450 991076028480332120231031130208.0981-9957-69-910.1007/978-981-99-5769-9(MiAaPQ)EBC30847607(Au-PeEL)EBL30847607(DE-He213)978-981-99-5769-9(PPN)272916617(EXLCZ)992864536300004120231031d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierTrivalent Discrete Surfaces and Carbon Structures[electronic resource] /by Hisashi Naito1st ed. 2023.Singapore :Springer Nature Singapore :Imprint: Springer,2023.1 online resource (113 pages)SpringerBriefs in the Mathematics of Materials,2365-6344 ;5Print version: Naito, Hisashi Trivalent Discrete Surfaces and Carbon Structures Singapore : Springer,c2023 9789819957682 Overview of this monograph -- Graph theory -- Topological crystals -- Negatively curved carbon structures -- Trivalent discrete surfaces -- Subdivisions of trivalent discrete surfaces -- Miscellaneous topics.This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects. .SpringerBriefs in the Mathematics of Materials,2365-6344 ;5Geometry, DifferentialDiscrete mathematicsDifferential GeometryApplications of Discrete MathematicsDiscrete MathematicsGeometry, Differential.Discrete mathematics.Differential Geometry.Applications of Discrete Mathematics.Discrete Mathematics.548.7Naito Hisashi732150MiAaPQMiAaPQMiAaPQBOOK9910760284803321Trivalent Discrete Surfaces and Carbon Structures3598784UNINA