Schiffer variations and Abelian differentials

Scott A. Wolpert

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arXiv · 1508.01100

Schiffer variations and Abelian differentials

Scott A. Wolpert

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Abstract

Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation expansion is presented for Abelian differentials. Schiffer's kernel function approach for deformations of a Green's function is followed.

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BibTeX RIS

Scott A. Wolpert. 2015-08-05. Schiffer variations and Abelian differentials. https://arxiv.org/abs/1508.01100

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