Eigenvalues and entropy of a Hitchin representation

• 成果类型: Article
• 署名作者: Potrie, Rafael; Sambarino, Andres
• 署名单位: Universidad de la Republica, Uruguay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0721-9
• 发表日期: 2017
• 页码: 885-925
• 关键词: hyperconvex representations; anosov-flows; components; SURFACES

摘要

We show that the critical exponent of a representation rho in the Hitchin component of PSL(d,R) is bounded above, the least upper bound being attained only in the Fuchsian locus. This provides a rigid inequality for the area of a minimal surface on rho\X where X is the symmetric space of PSL(d,R) The proof relies in a construction useful to prove a regularity statement: if the Frenet equivariant curve of rho is smooth, then rho is Fuchsian.