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• W2891247249 abstract "Let $pi:mc{X}to mc{T}$ be Teichmuller curve over Teichmuller space $mc{T}$, such that the fiber $mc{X}_z=pi^{-1}(z)$ is exactly the Riemann surface given by the complex structure $zin mc{T}$. For a fixed Riemannian manifold $M$ and a continuous map $u_0: Mto mc{X}_{z_0}$, let $E(z)$ denote the energy function of the harmonic map $u(z):Mto mc{X}_z$ homotopic to $u_0$, $zin mathcal T$. We obtain the first and the second variations of the energy function $E(z)$, and show that $log E(z)$ is strictly plurisubharmonic on Teichmuller space, from which we give a new proof on the Steinness of Teichmuller space. We also obtain a precise formula on the second variation of $E^{1/2}$ if $dim M=1$. In particular, we get the formula of Axelsson-Schumacher on the second variation of the geodesic length function. We give also a simple and corrected proof for the theorem of Yamada, the convexity of energy function $E(t)$ along Weil-Petersson geodesics. As an application we show that $E(t)^c$ is also strictly convex for $c>5/6$ and convex for $c=5/6$ along Weil-Petersson geodesics. We also reprove a Kerckhoff's theorem which is a positive answer to the Nielsen realization problem." @default.
• W2891247249 created "2018-09-27" @default.
• W2891247249 creator A5023050480 @default.
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• W2891247249 date "2018-09-01" @default.
• W2891247249 modified "2023-10-01" @default.
• W2891247249 title "Plurisubharmonicity and geodesic convexity of energy function on Teichmüller space" @default.
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• W2891247249 hasPublicationYear "2018" @default.
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