Index and nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces
Filippo Morabito
TL;DR
This paper extends the analysis of the Gauss map's index and nullity for Costa-Hoffman-Meeks minimal surfaces to higher genus values, establishing their non-degeneracy across all genera.
Contribution
It generalizes previous results to all genus values above 37, confirming the non-degeneracy of these minimal surfaces.
Findings
Gauss map index and nullity are computed for higher genus surfaces.
Costa-Hoffman-Meeks surfaces are non-degenerate for all genus values.
Results support the stability analysis of these minimal surfaces.
Abstract
The aim of this work is to extend the results of S. Nayatani about the index and the nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces for values of the genus bigger than 37. That allows us to state that these minimal surfaces are non degenerate for all the values of the genus in the sense of the definition of J. Perez and A. Ros.
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
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Differential Equations and Dynamical Systems