Timeline for Flapping wings: on a question of Kapouleas
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2021 at 22:23 | comment | added | Leo Moos | That's very neat, thanks again! | |
| Aug 24, 2021 at 18:19 | comment | added | Sebastian | Many thanks. Completeness of the family of surfaces means, that the family of induced Riemann surface structures converges to points in the boundary of the Teichmüller space at $\varphi=0,\tfrac{\pi}{2}.$ In particular, the family cannot be extended any further, and has a nice (degenerate) geometric limit by point (3.). I do not know if this family foliates the 3-sphere. Concerning the mean curvature: (4.) describes the dependence on $\varphi$ for $g\sim\infty$. It is possible to compute $H$ to arbitrary order (in $t=\frac{1}{2g+2}$) up to certain complicated integrals (multipolylogs) | |
| Aug 24, 2021 at 17:30 | comment | added | Leo Moos | I appreciate the added information. Congratulations on the preprint - it seems like a very interesting result! By the way, if I may add some questions: what does it means for a family of surfaces to be complete? Also, if I am not mistaken the deformations of the Clifford torus basically foliate the sphere. I am guessing this isn't true anymore here? Do your methods explain how $H$ changes with the angle $\varphi$? | |
| Aug 24, 2021 at 17:00 | history | answered | Sebastian | CC BY-SA 4.0 |