45. chen.li.ea:26:fourier
^^^^^^^^^^^^^^^^^^^^^^^^^

.. centered:: A Fourier approach to Gromov's filling area conjecture
.. centered:: Le Chen, Xiaolong Li and Yimin Zhong

**Abstract:** We prove that every compact connected Riemannian isometric
filling :math:`M` of a circle of length :math:`2\pi` satisfies

.. math::

   \operatorname{Area}(M) \geq \frac{14\zeta(3)}{\pi} \approx 5.35677,

regardless of orientability or topological types. Our new approach uses the
odd Fourier coefficients of the distance functions from boundary points. For
orientable fillings, we use a cubic resonant perturbation to obtain
:math:`\operatorname{Area}(M) > 5.40154`.

`Preprint <https://arxiv.org/abs/2609.08251>`_

:cite:`chen.li.ea:26:fourier` Le Chen, Xiaolong Li & Yimin Zhong (2026) 'A
Fourier approach to Gromov's filling area conjecture', *preprint
arXiv:2609.08251, 20 pages*

.. code-block:: bibtex

   @article{chen.li.ea:26:fourier,
      title         = {A Fourier approach to {G}romov's filling area conjecture},
      author        = {Le Chen and Xiaolong Li and Yimin Zhong},
      year          = {2026},
      month         = {September},
      journal       = {Preprint arXiv:2609.08251},
      url           = {http://arXiv.org/abs/2609.08251}
   }


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