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Honda Lab
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A lab that uses Ricci curvature to study how spaces collapse.
AboutAbout the lab
What remains when a space collapses?
The Honda Lab studies geometric analysis related to Ricci curvature, as well as collapsing theory.
Geometric analysis is a field that studies the shapes of figures and spaces using tools from differential equations and analysis.
From the perspective of convergence and collapsing theory for manifolds, the lab deals not only with Riemannian manifolds but also with more singular spaces.
Key terms
- Manifold
- A mathematical object for describing smoothly connected shapes and spaces. It generalizes surfaces to higher dimensions.
- Ricci curvature
- One of the quantities that describe how a space curves. It characterizes shape through the way volume grows.
- Collapsing theory
- A theory that studies how a sequence of shapes collapses into shapes of lower dimension.
ResearchResearch themes
The lab's research field is geometric analysis, with themes in geometric analysis related to Ricci curvature and collapsing theory. From the perspective of convergence and collapsing theory for manifolds, the lab investigates the relationship between how a space curves and its shape.
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MembersFaculty
- ProfessorShouhei HondaPublications ↗
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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: “Lidinoid surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Ricci Curvature and Collapsing Theory: “Modell einer Schraubenfläche konstanter negativer Krümmung -Schilling V, 4 - 231” Ramona Trusheim / CC BY-SA 3.0 (cropped)
- Related lab (Takatsu Lab): “Continuous optimal transport” Nicolas Papadakis / CC BY-SA 4.0 (cropped)
- Related lab (Ueda Lab): “Quintic 1” The original uploader was Floriang at German Wikipedia. / CC BY-SA 3.0 (cropped)
- Related lab (Konno Lab): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
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