发表机构
Korea Institute for Advanced Study (KIAS); Chongqing University of Technology; Chalmers University of Technology, University of Gothenburg（韩国高等科学研究院; 重庆理工大学; 哥德堡大学查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将双曲长度函数沿Teichmüller测地线的拟凸性推广到调和映射能量函数的两种情形，证明了相关拟凸性并推广了Masur的渐近增长结果，推导了能量函数的变分公式。
AI 中文摘要
双曲长度函数是Teichmüller空间上最基本的函数之一，且沿Teichmüller测地线具有拟凸性。本文针对两种自然情形下调和映射的能量函数研究相同问题，这类能量函数可视为长度函数的非线性高维类似物。对于固定定义域、目标为变化双曲曲面的情形，我们在填充假设下证明能量沿Teichmüller测地线具有拟凸性；此外，我们将Masur关于长度函数沿Jenkins-Strebel微分确定的Teichmüller测地线的渐近增长结果推广到能量函数。我们还证明了固定目标、定义域为变化双曲闭曲面的覆盖映射的拟凸性。我们推导了能量函数沿Teichmüller测地线的一阶和二阶变分公式，并解释了为何自然的全局结论是拟凸性而非严格凸性。
英文摘要
Hyperbolic length functions are among the most fundamental ones on Teichmüller space, and they are quasi-convex along Teichmüller geodesics. In this paper, we investigate the same question for energy functions of harmonic maps in two natural settings, which may be viewed as nonlinear and higher-dimensional analogs of the length functions. For a fixed domain and a varying hyperbolic target, we prove the energy is quasi-convex along Teichmüller geodesics under a filling hypothesis. Furthermore, we generalize Masur's result on asymptotic growth of the length function along the Teichmüller geodesic determined by a Jenkins-Strebel differential to the energy functions. We also prove the quasi-convexity for covering maps between closed hyperbolic surfaces with fixed target and varying domains. We derive first and second variation formulas of energy functions along Teichmüller geodesics and explain why the natural global statement is quasi-convexity rather than genuine convexity.
Comments57 pages. Comments are welcome
