Fix an almost-complex structure $J$ on $\mathbb{R}^{2n}.$ Let $u: (D^2, i) \to (\mathbb{R}^{2n}, J)$ be a $J$-holomorphic disk.
My question: can one prove an a-priori bound on the diameter of $u$ (say in terms of the norm of $J$)?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityFix an almost-complex structure $J$ on $\mathbb{R}^{2n}.$ Let $u: (D^2, i) \to (\mathbb{R}^{2n}, J)$ be a $J$-holomorphic disk.
My question: can one prove an a-priori bound on the diameter of $u$ (say in terms of the norm of $J$)?