Abstract
We prove that every J-holomorphic variational vector field can be realized as derivation \(\frac{d}{dt}_{|t=0}f_t\) where \((f_t)\) is a one parametric family of J-holomorphic discs. Furthermore, we discuss properness of an extremal J-holomorphic disc in a bounded pseudoconvex domain.
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Acknowledgements
Research of the author was supported in part by grants P1-0291, J1-9104 and BI-US/19-21-108 from ARRS, Republic of Slovenia. He would also like to thank Herve Gaussier and Franc Forstnerič for their useful comments while he was preparing the paper.
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Kuzman, U. On J-Holomorphic Variational Vector Fields and Extremal Discs. J Geom Anal 31, 8632–8640 (2021). https://doi.org/10.1007/s12220-020-00605-w
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DOI: https://doi.org/10.1007/s12220-020-00605-w