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In this chapter we survey the proof of Carleson’s \(\varepsilon ^2\) conjecture in the plane and its extension to higher dimensions. We also describe its connections with rectifiability and the so-called Faber-Krahn inequalities for the first eigenvalue of the Laplacian.

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Carleson’s \(\varepsilon ^2\) Conjecture in Higher Dimensions and Faber-Krahn Inequalities

  • 会议论文

  • 发表日期：

    2025年

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  • Xavier Tolsa

摘要

In this chapter we survey the proof of Carleson’s \(\varepsilon ^2\) conjecture in the plane and its extension to higher dimensions. We also describe its connections with rectifiability and the so-called Faber-Krahn inequalities for the first eigenvalue of the Laplacian.