Date of Submission

Winter 2024

Academic Program

Mathematics

Project Advisor 1

Charles Doran

Abstract/Artist's Statement

The study of Ricci flow in differential geometry provides a foundational approach to understandng the intrinsic geometry of surfaces through the evolution of curvature. By deforming the Riemannian metric over time, Hamilton’s Ricci flow enables surfaces to reach a state of uniform curvature, simplifying complex geometric structures and facilitating computational analysis. My thesis builds on this framework by visualizing the intrinsic unfolding of Ricci flow as it acts on discrete 3D meshes, illustrating how these structures conform to a 2D plane while preserving their geometric integrity. This visualization provides a unique perspective on the behavior of Ricci flow in transitioning complex surfaces from three to two dimensions. Through this approach we acquire insights into the nature of curvature while also showing its implications for practical applications, such as surface registration and shape analysis in fields such as computer graphics.

Open Access Agreement

On-Campus only

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.

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