正比例表示
Positively ratioed representations
摘要：
设S是亏格至少为2的闭可定向曲面，G是非紧型半单实代数群.我们考虑一类从S到G的基本群的表示，称为正比例表示。这些都是阿诺索夫表示的附加条件，某些相关的交比满足一个积极的性质。这种表示的例子包括希钦表示和极大表示。使用测地电流，我们表明，这些积极的比例表示相应的长度函数是良好的行为。特别是，我们证明了收缩不等式，所有这些积极的ratioed表示。
英文摘要：
Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain associated cross ratios satisfy a positivity property. Examples of such representations include Hitchin representations and maximal representations. Using geodesic currents, we show that the corresponding length functions for these positively ratioed representations are well-behaved. In particular, we prove a systolic inequality that holds for all such positively ratioed representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
