@phdthesis{oai:sucra.repo.nii.ac.jp:00018516,
 author = {髙野, 耕太},
 month = {},
 note = {45 p., 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., 1 Introduction 2
2 Preliminaries 5
2.1 Some notations . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Densities and approximate tangent spaces . . . . . . . . . . . 7
2.3 Varifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 The main theorem and its proof 11
3.1 The assertion of the main theorem . . . . . . . . . . . . . . . 11
3.2 Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Proof of the main theorem . . . . . . . . . . . . . . . . . . . . 17
3.4 Comparison with the Laplacian of a graph . . . . . . . . . . . 31
4 Inverse of a tangent-point radius and some examples 34
4.1 The explanation of the geometric meaning of the main theorem 34
4.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Comparisons with other generalizations of mean curvature 40
5.1 Comparison with curvature measures . . . . . . . . . . . . . . 40
5.2 Comparison with the variational mean curvature . . . . . . . . 42, 指導教員 : 長澤壯之, text, application/pdf},
 school = {埼玉大学},
 title = {A geometric representation of the generalized mean curvature},
 year = {2018},
 yomi = {タカノ, コウタ}
}