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2019 Fiscal Year Final Research Report

Geometric variational problems and discrete geometry with numerical analysis

Research Project

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Project/Area Number 26400067
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionNagoya University

Principal Investigator

Naito Hisashi  名古屋大学, 多元数理科学研究科, 准教授 (40211411)

Project Period (FY) 2014-04-01 – 2020-03-31
Keywordsdiscrete surfaces
Outline of Final Research Achievements

We study geometry of trivalent discrete surfaces. In paricular, we define vertex-wise Gauss and mean curvatures for trivalent discrete surfaces in 3-dimensional Euclidean spaces. In our study, we take Carbon nanotubes, Fullerens, and Mackay structures, and we show that the Mackay structure of type P is vertex-wise negatively curved, which is called "a negatively graphene" in material sciences and organic chemistry.
Moreover, we study subdivision of trivalent discrete surfaces. In particular, we show the Hausdorff convergence of the sequence of minimum energies of Mackay structures.

Free Research Field

離散幾何解析

Academic Significance and Societal Importance of the Research Achievements

従来の離散曲面論は,連続曲面の離散化として離散曲面を定義していた. この研究では,分子構造・結晶構造をモデルとした,本質的に離散な曲面を対象とし,その幾何学を展開したことに重要な意義がある. しかも,単純に曲率を定義するだけではなく,離散曲面の細分を定義することにより,収束理論への道を開いた. 一般に,分子構造・決s高構造のミクロな解析では離散的なオブジェクトとしてそれらを扱うが,収束理論を通じて,マクロな連続的なオブジェクトを扱うことができる可能性を示した.

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Published: 2021-02-19  

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