Karpukhin, Mikhail;
Stern, Daniel;
(2024)
From Steklov to Laplace: free boundary minimal surfaces with many boundary components.
Duke Mathematical Journal
, 173
(8)
pp. 1557-1629.
10.1215/00127094-2023-0041.
Preview |
Text
FBMS_paper_v6.pdf - Accepted Version Download (596kB) | Preview |
Abstract
In the present paper, we study sharp isoperimetric inequalities for the first Steklov eigenvalue σ1 on surfaces with fixed genus and large number k of boundary components. We show that as k → ∞ the free boundary minimal surfaces in the unit ball arising from the maximization of σ1 converge to a closed minimal surface in the boundary sphere arising from the maximization of the first Laplace eigenvalue on the corresponding closed surface. For some genera, we prove that the corresponding areas converge at the optimal rate log k k . This result appears to provide the first examples of free boundary minimal surfaces in a compact domain converging to closed minimal surfaces in the boundary, suggesting new directions in the study of free boundary minimal surfaces, with many open questions proposed in the present paper. A similar phenomenon is observed for free boundary harmonic maps associated to conformally-constrained shape optimization problems.
| Type: | Article |
|---|---|
| Title: | From Steklov to Laplace: free boundary minimal surfaces with many boundary components |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1215/00127094-2023-0041 |
| Publisher version: | http://dx.doi.org/10.1215/00127094-2023-0041 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Free boundary , Isoperimetric inequality , minimal surface , Steklov eigenvalues |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10194581 |
Archive Staff Only
 |
View Item |
