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We present a quantitative isolation property of the lifts of properly immersed geodesic planes in the frame bundle of a geometrically finite hyperbolic 
$3$-manifold. Our estimates are polynomials in the tight areas and Bowen–Margulis–Sullivan densities of geodesic planes, with degree given by the modified critical exponents.
$3$
-manifolds containing infinitely many totally geodesic surfaces
We prove that if a closed hyperbolic 
$3$
-manifold M contains infinitely many totally geodesic surfaces, then M is arithmetic.
