Eigenvalues and entropy of a Hitchin representation

Eigenvalues and entropy of a Hitchin representation We show that the critical exponent of a representation $$\rho $$ ρ in the Hitchin component of $${{\mathrm{PSL}}}(d,\mathbb {R})$$ 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 $$\rho \backslash X,$$ ρ \ X , where X is the symmetric space of $${{\mathrm{PSL}}}(d,\mathbb {R})$$ PSL ( d , R ) . The proof relies in a construction useful to prove a regularity statement: if the Frenet equivariant curve of $$\rho $$ ρ is smooth, then $$\rho $$ ρ is Fuchsian. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Inventiones mathematicae Springer Journals

Eigenvalues and entropy of a Hitchin representation

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Mathematics; Mathematics, general
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