## Tatsuya Miura

### MIURA, Tatsuya (**三浦 達哉**)

**三浦 達哉**)

Here is a personal research web page of Tatsuya Miura.

I am a mathematician, and currently an Associate Professor of the Department of Mathematics of the Tokyo Institute of Technology.

**E-mail address:**miura [at-sign] math.titech.ac.jp**Postal address:**2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JAPAN**Room number:**H210, Main Bldg., Ookayama campus (How to access)

### Research information

**Research field:**mathematics**Research areas:**geometric analysis, calculus of variations, differential equation and geometry, geometric inequality**Keywords and interests:**geometric higher-order variational problem (elastic curve/surface, bending energy, Willmore energy), geometric inequality (Li-Yau type inequality, Topping conjecture, isoperimetric inequality), geometric flow (elastic flow, surface diffusion flow, mean curvature flow), minimal surface, cut locus or medial axis, optimal transport...

Publication list is below. My complete CV is available in Researchmap (English ver.) Other links: Google Scholar, ORCID

Brief CV: I completed my PhD in September 2017 at the University of Tokyo under the supervision of Prof. Yoshikazu Giga, and was a postdoctoral fellow around 2018 in the group of Prof. Felix Otto at the Max Planck Institute for Mathematics in the Sciences in Leipzig. I became an assistant professor of the Tokyo Institute of Technology in 2019, and got promoted to an associate professor in 2021.

### News & Schedule

### News

**23rd January 2023:**New preprint with Kensuke Yoshizawa on general instability theory for curves including (p-)elastica.**4th July 2022:**Received the 2022 Tokyo Tech Challenging Research Award.

### Schedule

**30th January -- 1st February 2022:**Talk in The 40th Kyushu Symposium on Partial Differential Equations at Nishijin Plaza (Kyushu University).**4th -- 9th June 2023:**Invited to The 81st Fujihara Seminar Mathematical Aspects for Interfaces and Free Boundaries at Hilton Niseko Village, Hokkaido.**20th -- 25th August 2023:**Together with Tobias Ried and Jonas Sauer, I will organize a minisymposium "Nonlinear PDEs & Probability" in**16th -- 20th October 2023:**Talk in the Euro-Japanese Conference on Nonlinear Diffusion at ICMAT-UAM, Madrid (Spain).

### Publications

### Papers and Preprints (ordered by arXiv numbers)

(with Kensuke Yoshizawa)

**General rigidity principles for stab****le and minimal elastic curves**

submitted | arXiv:2301.08384(with Kensuke Yoshizawa)

**Pinned planar p-elasticae**

submitted | arXiv:2209.05721(with Minoru Tanaka)

**Delta-convex structure of the singular set of distance functions**

submitted | arXiv:2204.10449(with Kensuke Yoshizawa)

**Complete classification of planar p-elasticae**

submitted | arXiv:2203.08535(with Marius Müller and Fabian Rupp)

**Optimal thresholds for preserving embeddedness of elastic flows****Li-Yau type inequality for curves in any codimension****A diameter bound for compact surfaces and the Plateau-Douglas problem***Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)***23**(2022), no. 4, 1707--1721. | arXiv:2010.02797**Polar tangential angles and free elasticae***Math. Eng.***3**(2021), no. 4, Paper No. 034, 12 pp. (open access) | arXiv:2004.06497**Geometric inequalities involving mean curvature for c****losed****surfaces***Selecta Math. (N.S.)***27**(2021), Art. 80, 24 pp. | PDF | arXiv:2004.01409(with Felix Otto)

**Sharp boundary ε-regularity of optimal transport maps***Adv. Math.***381**(2021), Paper No. 107603, 65 pp. | arXiv:2002.08668(with Shinya Okabe)

**On the isoperimetric inequality and surface diffusion flow for multiply winding curves***Arch. Ration. Mech. Anal.***239**(2021), 1111--1129. (open access) | PDF | arXiv:1909.08816**Elastic curves and phase transitions***Math. Ann.***376**(2020), no. 3--4, 1629--1674. | PDF | arXiv:1710.05890**Overhanging of membranes and filaments adhering to periodic graph substrates***Phys. D***355**(2017), 34--44. | arXiv:1612.08532**A characterization of cut locus for C^1 hypersurfaces***NoDEA Nonlinear Differential Equations Appl.***23**(2016), no. 6, Art. 60, 14 pp. | PDF | arXiv:1509.00546**Singular perturbation by bending for an adhesive obstacle problem***Calc. Var. Partial Differential Equations***55**(2016), no. 1, Art. 19, 24 pp. | PDF | arXiv:1502.04212**An example of a mean-convex mean curvature flow developing infinitely many singular epochs***J. Geom. Anal.***26**(2016), no. 4, 3019--3026. | PDF | arXiv:1411.6249

### Misc (*peer-reviewed)

*(with Y. Goto, G. Hosono, and H. Kodama)

**A suggestion of peripheral curves on hard contact lenses**(in Japanese)*Suurikagaku Jissenkenkyu Letter*(2018), LMSR 2018-1.**On minimizers of Euler's elastica energy with an adhesion effect***RIMS Kôkyûroku*(2017), no. 2046, 50--59.**On the shapes of elastic curves adhering to substrates**(in Japanese)*Proceedings of the 38th Young Researchers Seminar on Evolution Equations*, 2016.**A characterization of cut locus for C^1 hypersurfaces**(in Japanese)*Proceedings of the 37th Young Researchers Seminar on Evolution Equations*, 2015.

### Scientific activities

### Organizing seminars

東工大数理解析セミナー (Tokyo Tech Mathematical Analysis Seminar) 2019 February -- present.

非線形解析セミナー@大岡山 (Nonlinear Analysis Seminar at Ookayama) 2019 February -- present.

### Editorial board

Kodal Mathematical Journal 2021 July -- present.

### External links

### Misc

Richard E. BORCHERDS (YouTube) / Questions and Answers 1

The Euler Archive / 20 October, 1742 Letter from D. Bernoulli to Euler

Simons Foundation / John W. Milnor (Lectures on Differential Topology, 1965)

### Roots

My mathematical ancestors according to the Mathematics Genealogy Project:

Tatsuya Miura --> Yoshikazu Giga --> Daisuke Fujiwara --> Seizô Itô --> Shokichi Iyanaga --> Teiji Takagi --> David Hilbert, and you can chase more by seeing the top image here.I have an Erdős number of 4 due to MathSciNet as of 1st May 2021:

Paul Erdős --> David Preiss --> Giovanni Alberti --> Felix Otto --> Tatsuya Miura.

剱持智哉氏による 日本語 LaTeX 情報など

2022年度東工大挑戦的研究賞授賞式の写真