Report
A counterexample to Nirenberg's conjecture on closed asymptotic curves
| Τίτλος: | A counterexample to Nirenberg's conjecture on closed asymptotic curves |
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| Συγγραφείς: | Banks, Harrison, Ghomi, Mohammad, Qiu, Hongda, Raffaelli, Matteo |
| Έτος έκδοσης: | 2026 |
| Θεματικοί όροι: | Differential Geometry, Primary 53A04, 53A05, Secondary 35L10, 53C24 |
| Περιγραφή: | We construct a smooth embedded annulus in $R^3$ with negative Gauss curvature in its interior whose boundary consists of two strictly convex curves in planes tangent to the annulus, and which contains two closed asymptotic curves. This gives a counterexample to a 1962 conjecture of Nirenberg. The construction is based on Lelieuvre's formula, which yields a closed curve that is then realized as an asymptotic curve on a ruled annulus. The second asymptotic curve is obtained from the periodic solution of a Riccati equation. 10 pages, 3 figures |
| Τύπος εγγράφου: | Working Paper |
| DOI: | 10.48550/arXiv.2610.13848 |
| Σύνδεσμος πρόσβασης: | https://arxiv.org/abs/2610.13848 |
| Αριθμός Καταχώρησης: | edsarx.2610.13848 |
| Βάση Δεδομένων: | arXiv |
| DOI: | 10.48550/arXiv.2610.13848 |
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