Variational Formulas llnder C^2-movements

2009-04-07T07:05:21Z

2009-04-07T07:05:21Z

1990-03

We shall investigate the change of function-theoretic quantities as a Riemann surface deforms smoothly. As a smooth deformation, we consider Riemann surfaces with conformal structures decided by Beltrami differentials depending differentiably on parameters. Function-theoretic quantities are often represented by meromorphic differentials with specific kind of boundary behavior. We show here that their differentials vary differentiably and obtain variational formulas of function-theoretic quantities. We take up a recovering deformation as a quasiconformal deformation and apply our results.

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Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology, Series of Science and Technology, Vol.38 (1989) pp.23-34

http://hdl.handle.net/10212/1907

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