{"created":"2023-05-15T15:29:00.856770+00:00","id":18516,"links":{},"metadata":{"_buckets":{"deposit":"236b7398-ce81-431e-bce6-1628ef7660fe"},"_deposit":{"created_by":15,"id":"18516","owners":[15],"pid":{"revision_id":0,"type":"depid","value":"18516"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00018516","sets":["94:429:431:432:925"]},"author_link":["29504"],"item_113_alternative_title_1":{"attribute_name":"タイトル（別言語）","attribute_value_mlt":[{"subitem_alternative_title":"一般化された平均曲率ベクトルの積分平均極限を用いた幾何学的表示"}]},"item_113_biblio_info_9":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2018","bibliographicIssueDateType":"Issued"}}]},"item_113_date_35":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2019-02-08","subitem_date_issued_type":"Created"}]},"item_113_date_granted_20":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2018-03-23"}]},"item_113_degree_grantor_22":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"埼玉大学"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"12401","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_113_degree_name_21":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(理学)"}]},"item_113_description_13":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_description":"45 p.","subitem_description_type":"Other"}]},"item_113_description_23":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"A varifold is a generalization of a differential manifold using Radon measures. The theory of varifolds is a central topic in geometric measure theory. Any varifold possesses a notion similar to “the area”, and the generalized mean curvature is defined through the first variation of “the area”. If a varifold has C2 regularity, then the generalized mean curvature coincides with the classical mean curvature. Furthermore, if the generalized mean curvature vector has some integrablity, then we obtain some regularity of the varifold. In this sense the generalized mean curvature contains information concerning its shape. However, it is not known that generalized mean curvature vector is represented without the first variation. In this paper, under the C1,α regularity condition, for α > 1/3, we give a geometric representation of the generalized mean curvature using a limit of integral averages suggested by the Menger curvature.","subitem_description_type":"Abstract"}]},"item_113_description_24":{"attribute_name":"目次","attribute_value_mlt":[{"subitem_description":"1 Introduction 2\n2 Preliminaries 5\n2.1 Some notations . . . . . . . . . . . . . . . . . . . . . . . . . . 5\n2.2 Densities and approximate tangent spaces . . . . . . . . . . . 7\n2.3 Varifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7\n3 The main theorem and its proof 11\n3.1 The assertion of the main theorem . . . . . . . . . . . . . . . 11\n3.2 Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13\n3.3 Proof of the main theorem . . . . . . . . . . . . . . . . . . . . 17\n3.4 Comparison with the Laplacian of a graph . . . . . . . . . . . 31\n4 Inverse of a tangent-point radius and some examples 34\n4.1 The explanation of the geometric meaning of the main theorem 34\n4.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35\n5 Comparisons with other generalizations of mean curvature 40\n5.1 Comparison with curvature measures . . . . . . . . . . . . . . 40\n5.2 Comparison with the variational mean curvature . . . . . . . . 42","subitem_description_type":"Other"}]},"item_113_description_25":{"attribute_name":"注記","attribute_value_mlt":[{"subitem_description":"指導教員 : 長澤壯之","subitem_description_type":"Other"}]},"item_113_description_33":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_113_description_34":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_113_dissertation_number_19":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第1088号"}]},"item_113_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24561/00018486","subitem_identifier_reg_type":"JaLC"}]},"item_113_publisher_11":{"attribute_name":"出版者名","attribute_value_mlt":[{"subitem_publisher":"埼玉大学大学院理工学研究科"}]},"item_113_publisher_12":{"attribute_name":"出版者名（別言語）","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Science and Engineering, Saitama University"}]},"item_113_record_name_8":{"attribute_name":"書誌","attribute_value_mlt":[{"subitem_record_name":"博士論文（埼玉大学大学院理工学研究科（博士後期課程））"}]},"item_113_text_3":{"attribute_name":"著者 ローマ字","attribute_value_mlt":[{"subitem_text_value":"TAKANO, Kouta"}]},"item_113_text_31":{"attribute_name":"版","attribute_value_mlt":[{"subitem_text_value":"[出版社版]"}]},"item_113_text_36":{"attribute_name":"アイテムID","attribute_value_mlt":[{"subitem_text_value":"GD0000993"}]},"item_113_text_4":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"埼玉大学大学院理工学研究科（博士後期課程）理工学専攻"}]},"item_113_text_5":{"attribute_name":"著者 所属（別言語）","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Science and Engineering, Saitama University"}]},"item_113_version_type_32":{"attribute_name":"出版タイプ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"髙野, 耕太","creatorNameLang":"ja"},{"creatorName":"タカノ, コウタ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2019-02-08"}],"displaytype":"detail","filename":"GD0000993.pdf","filesize":[{"value":"223.6 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"GD0000993.pdf","objectType":"fulltext","url":"https://sucra.repo.nii.ac.jp/record/18516/files/GD0000993.pdf"},"version_id":"fd89969d-c8de-4923-9633-503f336285ba"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"doctoral thesis","resourceuri":"http://purl.org/coar/resource_type/c_db06"}]},"item_title":"A geometric representation of the generalized mean curvature","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A geometric representation of the generalized mean curvature","subitem_title_language":"en"}]},"item_type_id":"113","owner":"15","path":["925"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2019-02-08"},"publish_date":"2019-02-08","publish_status":"0","recid":"18516","relation_version_is_last":true,"title":["A geometric representation of the generalized mean curvature"],"weko_creator_id":"15","weko_shared_id":-1},"updated":"2023-07-31T07:16:26.295554+00:00"}