Publication
CMC surfaces condensing to geodesic rays and segments in Riemannian manifolds
AbstractWe construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces cannot exist in Euclidean space, but we show that the gradient of the ambient scalar curvature acts as a ‘friction term’ which permits the usual analytic gluing construction to be carried out.
Download publicationRelated Resources
See what’s new.
2021
Neural UpFlow: A Scene Flow Learning Approach to Increase the Apparent Resolution of Particle-Based LiquidsIn this research, we introduce a data-driven approach to increase the…
2023
Learning from and Inspiring Women at Girl Geek XDr. Tonya Custis shares how she learned about management and strategy…
2011
Building Information Modeling and Heritage DocumentationDespite the widespread adoption of building information modeling (BIM)…
2018
Investigating How Online Help and Learning Resources Support Children’s Use of 3D Design Software3D design software is increasingly available to children through…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us