On Tonelli periodic orbits with low energy on surfaces

@article{Asselle2016OnTP,
  title={On Tonelli periodic orbits with low energy on surfaces},
  author={Luca Asselle and Marco Mazzucchelli},
  journal={Transactions of the American Mathematical Society},
  year={2016}
}
<p>We prove that on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> possesses a periodic orbit that is a local minimizer of the free-period action functional on every energy level belonging to the… 

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