Gromov’s Schwarz lemma as an estimate of the gradient for holomorphic curves

  • Marie-Paule Muller
Part of the Progress in Mathematics book series (PM, volume 117)


In a symplectic manifold (M 2n , ω) with a tamed almost complex structure J, the 2-form ω induces an area form on (immersed) J-curves f: (Σ, i) → (M, J), where (Σ, i) is a Riemann surface which will be closed, open or compact with boundary, according to the context. The image f(Σ) will be denoted by S. Throughout this chapter, we shall assume that S is contained in a fixed compact subset of M.


Sectional Curvature Isoperimetric Inequality Compact Riemann Surface Holomorphic Curve Holomorphic Curf 
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© Springer Basel AG 1994

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  • Marie-Paule Muller

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