papers

Some of my papers can be downloaded here. If you are interested in our other works, please contact me.

Refereed papers

1. Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids, Journal of Math-for-Industry 4B (2012) 109-118 (with Wayne Rossman).   comment (only in Japanese)

2. Discrete maximal surfaces with singularities in Minkowski space, Differential Geometry and its Applications 43 (2015) 130-154.   comment (only in Japanese)

3. Bour surface companions in space forms, Proceedings of the International Conference on Geometry, Integrability and Quantization 17 (2016), 256-269 (with Erhan Güler and Shotaro Konnai).   comment (only in Japanese)

4. Semi-discrete surfaces of revolution, Kobe Journal of Mathematics 34 (2017), no.1-2, 13-26.   comment (only in Japanese)

5. Semi-discrete constant mean curvature surfaces of revolution with singularities in Minkowski space (with Christian Müller), Proceedings of the International Conference on Geometry, Integrability and Quantization 18 (2017), 191-202.   comment (only in Japanese)

6. Discrete linear Weingarten surfaces and their singularities in Riemannian and Lorentzian spaceforms, Advanced Studies in Pure Mathematics, Vol. 78 (2018), 383-410 (with Wayne Rossman).   comment (only in Japanese)

7. Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications, Differential Geometry and its Applications 54 Part A (2017), 264-281 (with Yuta Ogata).   comment (only in Japanese)

8. Weierstrass-type representations for timelike surfaces, Advanced Studies in Pure Mathematics, Vol. 78 (2018), 449-469.   comment (only in Japanese)

9. Trivalent maximal surfaces in Minkowski space, In: M. Cañadas-Pinedo, J. Flores, F. Palomo (eds) Lorentzian Geometry and Related Topics, Springer Proceedings in Mathematics & Statistics Vol. 211 (2018), 169-184 (with Wai Yeung Lam)   comment (only in Japanese)

10. Semi-discrete linear Weingarten surfaces and their singularities in Riemannian and Lorentzian spaceforms, Osaka Journal of Mathematics 57 (2020), 169-185 (with Wayne Rossman).   comment (only in Japanese)

11. 離散曲面の微分幾何, 日本数学会『数学』第73巻第1号 (2021), 1-21 (with Wayne Rossman).   comment (only in Japanese)

12. Semi-discrete maximal surfaces with singularities in Minkowski space, Springer Proceedings in Mathematics & Statistics Vol. 349 (2021), 263-280.   comment (only in Japanese)

13. Discrete Weierstrass-type representations, Discrete & Computational Geometry 70 (2023), 816-844 (with Mason Pember and Denis Polly).

Book

1. Discrete isothermic surfaces in Lie sphere geometry (with Joseph Cho, Kosuke Naokawa, Yuta Ogata, Mason Pember and Wayne Rossman), to appear in Lecture Notes in Mathematics.

Book (Chapter)

1. A first step to two topics in discretizations of surfaces in Euclidean space, In: Anam Lecture Notes in Mathematics 2 (2020), 1-35.

Non-refereed papers

1. Weierstrass representation for semi-discrete minimal surfaces, 第59回幾何学シンポジウム予稿集, pp.27-29.

2. Weierstrass representation for semi-discrete minimal surfaces, and comparison of three discretized catenoids, COE Lecture Note Vol. 41, p.68.

3. Weierstrass representation for semi-discrete minimal surfaces, 第9回数学総合若手研究集会テクニカルレポート, pp.105-108.

4. Discrete maximal surfaces with singularities in Minkowski space, COE Lecture Note Vol. 51, p.73.

5. ミンコフスキー空間内の特異点を持つ離散極大曲面について, 第10回数学総合若手研究集会テクニカルレポート, pp.213-216.

6. Weierstrass representation for semi-discrete minimal surfaces, RIMS kokyuroku. No.1868, pp.121-130.

7. 特異点を持つ曲面の離散化, 第61回幾何学シンポジウム予稿集, pp.34-37.

8. 離散線形Weingarten曲面について  (with Wayne Rossman, December 11, 2015 version), proceedings of a workshop "Geometry and Analysis" held in Fukuoka, pp.1-12.

Remark (in Japanese). 8.には内容を少しずつ加筆していきたいと考えています．日本語で読める曲面の離散微分幾何学のノートを作成することが目標です．誰が読むか分からないけど...

9. 三価グラフの極大曲面, 第63回幾何学シンポジウム予稿集, 157-160.

10. Discrete linear Weingarten surfaces with singularities: a survey, Proceedings of The 21st International Workshop on Hermitian Symmetric Spaces and Submanifolds 21 (2017), 43-51.

11. 4色定理の証明 -小さな誤りから大きな問題への道- (with Wayne Rossman), 数学セミナー (日本評論社), 2018年9月号, 43-47.

12. 3次元ミンコフスキー空間内の離散空間的平均曲率一定曲面, RIMS kokyuroku. No.2152, pp.1-15.

13. 3次元ユークリッド空間内の半離散ガウス曲率負一定曲面について (with Shunri Morikita), to appear in RIMS Kokyuroku.

Edited Proceedings

1. The 27th Osaka City University International Academic Symposium "Mathematical Science of Visualization, and Deepening of Symmetry and Moduli", OCAMI Reports (2021), Vol. 1 (96 pages).

Remark. This is a textbook about recent progress in discrete isothermic surfaces using Lie sphere geometric techniques.

In progress

1. The DPW method for discrete constant mean curvature surfaces in Lorentz-Minkowski space (with Masaya Hara, Phillip Käse, Naoya Suda, and Wayne Rossman).

2. Discrete timelike minimal surfaces and discrete wave equations (with Joseph Cho, Wayne Rossman, and Seong-Deog Yang). 

3. Discrete minimal surfaces: Old and new (with Wai Yeung Lam).

4. Weierstrass-type representations of timelike surfaces (with Masaya Hara, Denis Polly, and Sakuma Takeshita).

5. Semi-discrete timelike isothermic surfaces.

6. On the DPW method for semi-discrete CMC surfaces (with Wolfgang Carl).

7. TBA (曲面の微分幾何と離散微分幾何, with Wayne Rossman).

Remark. 曲面の微分幾何・離散微分幾何についての教科書です．2021年2026年3月に執筆完了を目指しています．

8. Curvatures of semi-discrete K-surfaces (with Shunri Morikita).

9. Bäcklund transformations of space curves, and semi-discrete K-surfaces.

10. Discrete minimal Darboux transformations (with Sakuma Takeshita).

11. On discrete timelike constant mean curvature surfaces (with Joseph Cho).

Thesis

1. Construction of discrete constant mean curvature surfaces, master thesis.

Remark. This thesis consists of a part of my paper named 

・Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications.

2. Differential Geometric Aspects of Discrete and Semi-discrete surfaces, Ph.D thesis (an official summary of this thesis is available for inspection in only Japanese, and the "unofficial" brief introduction of all chapters in English is available from here).

Remark. This thesis consists of the following papers:

・Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids,

・Discrete maximal surfaces with singularities in Minkowski space,

・Semi-discrete maximal surfaces with singularities in Minkowski space,

・Bour surface companions in space forms,

・(a part of) Discrete linear Weingarten surfaces and their singularities in Riemannian and Lorentzian spaceforms,

・(a part of) Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications.