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Pseudometrics on world lines

Consider the space $W$ of smooth time-like curves in $\mathbb{R}^{n,1}$ with fixed ends. Given $\gamma\in W$, consider the space $T_\gamma$ of all smooth normal fields along $\gamma$; one may think ...
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Harmonic maps into de Sitter Space

I am looking some references on the existence and non-existence of (space-like) harmonic maps solving the Dirichlet into the de-Sitter space. More precisely: Let, for $n\geq 3$, $$dS^n=\{ u\in \...
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Further directions in representations of surface group into a Lie group

$\DeclareMathOperator\SL{SL}\DeclareMathOperator\PSL{PSL}$I studied the interpretation of Teichmuller space as a representation space for surface groups in $\PSL(2,\mathbb{R})$. Now I am planning to ...
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