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Статья

Local properties of J-complex curves in Lipschitz-continuous structures

Mathematische Zeitschrift. 2011. Vol. 268. No. 3-4. P. 1159-1210.
Ivashkovich S., V. Shevchishin.

We prove the existence of primitive curves and positivity of intersections of J-complex curves for Lipschitz-continuous almost complex structures. These results are deduced from the Comparison Theorem for J-holomorphic maps in Lipschitz structures, previously known for J of class C1,Lip . We also give the optimal regularity of curves in Lipschitz structures. It occurs to be C1,LnLip , i.e. the first derivatives of a J-complex curve for Lipschitz J are Log-Lipschitz-continuous. A simple example that nothing better can be achieved is given. Further we prove the Genus Formula for J-complex curves and determine their principal Puiseux exponents (all this for Lipschitz-continuous J-s).