Some estimates related to Oh's conjecture for the Clifford tori in CP^n

Details Some estimates related to Oh's conjecture for the Clifford tori in CP^n Some estimates related to Oh's conjecture for the Clifford tori in CP^n

2003-11-26

arxiv.org/abs/math/0311460v1

Mathematics

Differential Geometry

Scientific paper

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 $a_2=3/\pi$ 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 $a_2= 3/\pi$ is the best one we know.

Affiliated with

Also associated with

No associations

Rating

Some estimates related to Oh's conjecture for the Clifford tori in CP^n does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some estimates related to Oh's conjecture for the Clifford tori in CP^n, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some estimates related to Oh's conjecture for the Clifford tori in CP^n will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-122516