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Analysis 1 (Partial Differential Equations, Geometric Analysis, Calculus of Variations) Lab (Tatsuya Miura)
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The lab studies the shapes of curves and surfaces using the calculus of variations.
AboutAbout the lab
Reading the shapes of flexible curves through equations
The Miura Lab studies nonlinear partial differential equations in the field of analysis.
Its main themes are the calculus of variations, the theory of elastic curves (curves like a flexible wire), and geometric analysis.
Including through collaborative research, the lab investigates how the shapes of curves and surfaces are determined and how they change over time.
Key terms
- Calculus of variations
- A method for finding and studying shapes or functions that minimize a quantity such as energy
- Elastic curve
- A flexible, wire-like curve whose shape is determined so as to minimize its bending energy
- Geometric analysis
- A field that uses tools of analysis, such as differential equations, to study the properties of geometric objects
ResearchResearch themes
The lab studies nonlinear partial differential equations, in particular the calculus of variations, the theory of elastic curves, and geometric analysis.
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MembersFaculty
- Associate ProfessorTatsuya Miura
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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: “Elastica-ExperimentalCurveShapesAndForces” Klemen Cotic / CC BY-SA 3.0 (cropped)
- Geometric inequalities for curves and surfaces: “Rectangular elastica and lemniscatic sine” Jacob Rus / CC BY-SA 4.0 (cropped)
- Related lab (Analysis 2 (Stochastic Analysis, Stochastic Control) Lab (Yushi Hamaguchi)): “Alpha-stable-levy” Thomas Steiner and Martin Keller-Ressel / CC BY-SA 2.5 (cropped)
- Related lab (Analysis 1 (Theory of Partial Differential Equations, Mean Curvature Flow) Lab (Keisuke Takasao)): “Reflection in a soap bubble edit” Brocken Inaglory. The image was edited by user:Alvesgaspar / CC BY-SA 3.0 (cropped)
- Related lab (Analysis 1 (Real Analysis) Lab (Yohei Tsutsui)): “Fourier Series-Square wave 3 H” Saisundar.s / CC BY-SA 4.0 (cropped)
- Related lab (Analysis 2 (Stochastic Analysis) Lab (Seiichiro Kusuoka)): “Girsanov” Martin Keller-Ressel (uploaded by Thomas Steiner) / CC BY-SA 3.0 (cropped)
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