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We review basic facts about meromorphic differentials that will be needed later on for the analytic construction of spectral networks. In particular, quadratic differentials induce natural decompositions of surfaces that lead to triangulations, thereby providing insight into some of its differential geometric aspects. Standard references for the role of quadratic differentials in Teichmüller theory include (Gardiner, Teichmüller theory and quadratic differentials. Pure and Applied Mathematics. John Wiley & Sons, 1987. ISBN: 0-471-84539-6) or (Strebel, Quadratic differentials, Vol. 5. Ergeb. Math. Grenzgeb., 3. Folge. Springer, Cham, 1984).

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Differentials on a Riemann Surface

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  • 出版模式：

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  • 发表日期：

    2026年

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  • Clarence Kineider,
  • Georgios Kydonakis,
  • Eugen Rogozinnikov,
  • Valdo Tatitscheff,
  • Alexander Thomas

摘要

We review basic facts about meromorphic differentials that will be needed later on for the analytic construction of spectral networks. In particular, quadratic differentials induce natural decompositions of surfaces that lead to triangulations, thereby providing insight into some of its differential geometric aspects. Standard references for the role of quadratic differentials in Teichmüller theory include (Gardiner, Teichmüller theory and quadratic differentials. Pure and Applied Mathematics. John Wiley & Sons, 1987. ISBN: 0-471-84539-6) or (Strebel, Quadratic differentials, Vol. 5. Ergeb. Math. Grenzgeb., 3. Folge. Springer, Cham, 1984).