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Upper bounds of the sum of Lyapunov exponents on Teichmüller curves
YU Fei * #
School of Mathematical Sciences, Zhejiang University, Hangzhou 310007
*Correspondence author
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Funding: Ph.D. Programs Foundation of Ministry of Education of China （No.20130121120042）
Opened online:16 May 2017
Accepted by: none
Citation: YU Fei.Upper bounds of the sum of Lyapunov exponents on Teichmüller curves[OL]. [16 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733747
 
 
We get anupper bound of the slope of each graded quotient for theHarder-Narasimhan filtration of the Hodge bundle of a Teichmüller curve. As an application, we show that the sum ofLyapunov exponents of a Teichmüller curve does not exceed${(g+1)}/{2}$, with equality reached if and only if the curve liesin the hyperelliptic locus induced from$mathcal{Q}(2k_1,...,2k_n,-1^{2g+2})$ or it is some specialTeichm"{u}ller curve in $Omegamathcal{M}_g(1^{2g-2})$.
Keywords:Lyapunov exponents; Teichmüller curves; Vector bundles
 
 
 

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