Some estimates related to Oh's conjecture for the Clifford tori in CP^n
| dc.creator | Goldstein, Edward | |
| dc.date | 2003-11-26 | |
| dc.date.accessioned | 2026-07-07T05:03:17Z | |
| dc.date.available | 2026-07-07T05:03:17Z | |
| dc.description | This note is motivated by Y.G. Oh's conjecture that the Clifford torus $L_n$ in $\mathbb{C}P^n$ minimizes volume in its Hamiltonian deformation class. We show that there exist explicit positive constants $a_n$ depending on the dimension with $a_2=3/π$ such that for any Lagrangian torus $L$ in the Hamiltonian class of $L_n$ we have $vol(L) \geq a_n vol (L_n)$. The proof uses the recent work of C.H. Cho on Floer homology of the Clifford tori. A formula from integral geometry enables us to derive the estimate. We wish to point out that a general lower bound on the volume of $L$ exists from the work of C. Viterbo. Our lower bound $a_2= 3/π$ is the best one we know. | |
| dc.identifier | https://arxiv.org/abs/math/0311460 | |
| dc.identifier | http://arxiv.org/abs/math/0311460 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69351 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53XX | |
| dc.title | Some estimates related to Oh's conjecture for the Clifford tori in CP^n | |
| dc.type | text |