Non-periodic Riemann examples with handles
Filippo Morabito, Martin Traizet
TL;DR
This paper demonstrates the existence of new non-periodic minimal surfaces with infinitely many ends, including finite and infinite genus examples, expanding the known landscape of minimal surface configurations.
Contribution
It introduces 1-parameter families of non-periodic, embedded minimal surfaces with infinitely many ends, including finite and infinite genus cases.
Findings
Existence of non-periodic minimal surfaces with infinitely many ends
Construction of finite genus examples
Development of quasi-periodic infinite genus examples
Abstract
We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals