Tatsuya Miura

MIURA, Tatsuya (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)

Photo in 2022. One of the two is me.

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

Schedule

Publications

Papers and Preprints (ordered by arXiv numbers)

  1. (with Kensuke Yoshizawa)
    General rigidity principles for stable and minimal elastic curves
    submitted | arXiv:2301.08384

  2. (with Kensuke Yoshizawa)
    Pinned planar p-elasticae
    submitted | arXiv:2209.05721

  3. (with Minoru Tanaka)
    Delta-convex structure of the singular set of distance functions
    submitted | arXiv:2204.10449

  4. (with Kensuke Yoshizawa)
    Complete classification of planar p-elasticae
    submitted | arXiv:2203.08535

  5. (with Marius Müller and Fabian Rupp)
    Optimal thresholds for preserving embeddedness of elastic flows
    submitted | arXiv:2106.09549

  6. Li-Yau type inequality for curves in any codimension
    submitted | arXiv:2102.06597

  7. 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

  8. Polar tangential angles and free elasticae
    Math. Eng. 3 (2021), no. 4, Paper No. 034, 12 pp. (open access) | arXiv:2004.06497

  9. Geometric inequalities involving mean curvature for closed surfaces
    Selecta Math. (N.S.) 27 (2021), Art. 80, 24 pp. | PDF | arXiv:2004.01409

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

  11. (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

  12. Elastic curves and phase transitions
    Math. Ann. 376 (2020), no. 3--4, 1629--1674. | PDF | arXiv:1710.05890

  13. Overhanging of membranes and filaments adhering to periodic graph substrates
    Phys. D 355 (2017), 34--44. | arXiv:1612.08532

  14. 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

  15. 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

  16. 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)

  1. *(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.

  2. On minimizers of Euler's elastica energy with an adhesion effect
    RIMS Kôkyûroku (2017), no. 2046, 50--59.

  3. On the shapes of elastic curves adhering to substrates (in Japanese)
    Proceedings of the 38th Young Researchers Seminar on Evolution Equations, 2016.

  4. A characterization of cut locus for C^1 hypersurfaces (in Japanese)
    Proceedings of the 37th Young Researchers Seminar on Evolution Equations, 2015.

Scientific activities

External links

Roots