| Abstract: |
| We consider a class of functionals that depends on two arguments, whose partial map with respect to one of the arguments achieves its minimum, and for which
the Palais-Smale condition is only partially satisfied in the other variable. Under some mild further assumption, we show existence of a global minimizer and uniqueness of critical points by using a new mountain pass theorem.
This abstract functional framework can be applied to the geometric question of parametrizing the
moduli space of minimal immersions in $3$-hyperbolic manifolds by using suitable data arising from the second fundamental forms of the immersion. |
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