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Tonegawa Lab
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A lab that uses analytic methods to study minimal surfaces and mean curvature flow.
AboutAbout the lab
Exploring surfaces and their motion through analysis.
The Tonegawa Lab studies elliptic and parabolic partial differential equations, geometric measure theory, and its applications.
The calculus of variations, the Allen–Cahn equation, and the Cahn–Hilliard equation are also objects of study.
Minimal surfaces and mean curvature flow are also among the main research themes.
An introductory book on Brakke's mean curvature flow (Brakke flow) has also been written.
Key terms
- Partial differential equation
- An equation expressing the relationship between a function of several variables and its rates of change (partial derivatives)
- Geometric measure theory
- A field of mathematics that extends the notions of area and volume so that surfaces with corners or sharp points can also be treated
- Mean curvature flow
- A way of changing in which each point of a surface moves according to the local bending (mean curvature) at that location
ResearchResearch themes
The lab studies elliptic and parabolic partial differential equations, geometric measure theory and its applications, and the calculus of variations. The Allen–Cahn equation, the Cahn–Hilliard equation, minimal surfaces, and mean curvature flow are also objects of study.
*Illustrative imageTheory of Flows in Which Surfaces Shrink
Mean curvature flow, in which a surface moves in the direction that reduces its area like a soap film, develops singularities and branching along the way. The lab works with weak solutions that remain meaningful even so (Brakke flow), and proves results on the smoothness at the end of the flow and on its existence.
*Illustrative imageInterface Motion and Coarsening
Using partial differential equations, the lab describes the phenomenon in which the boundary between two substances moves and the pattern becomes coarser, as well as the flow of an interface that moves while meeting a wall at a fixed angle, and mathematically investigates the existence and properties of their solutions.
*Illustrative imageInstability of Singularities of Minimal Surfaces
Minimal surfaces, which locally minimize area, can have singularities where flat surfaces intersect. The lab shows that when a small perturbation is added there and a flow is started, the shape is not preserved and breaks apart.
MembersFaculty
The members of the Tonegawa Lab consist of faculty members, researchers, and students in the doctoral and master's programs.As of 2026
- ProfessorTonegawa TonegawaPublications ↗
VoicesStudent voices
Compiled from answers by students who were in the lab. Ratings and reviews reflect individual students' experiences, not the lab's official views.
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped)
- Theory of Flows in Which Surfaces Shrink: “Soap Films” Ryan Somma / CC BY-SA 2.0 (cropped)
- Interface Motion and Coarsening: “Grgr3d small” Cenna / Public domain (cropped)
- Instability of Singularities of Minimal Surfaces: “Schwarz P Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (小野寺研究室): “Minimalfläche mit Seifenhaut Tetraeder 0326” Bin im Garten / CC BY-SA 3.0 (cropped)
- Related lab (三浦英之研究室): “Yakushima Island Von Karman Vortex street Oct 12 2012” NASA, MODIS Rapid Response System / Public domain (cropped)
- Related lab (本多研究室): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (鈴木研究室): “Complex zeta” Jan Homann / Public domain (cropped)
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