On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets

  • Michiel van den Berg

    University of Bristol, UK
  • Vincenzo Ferone

    Università degli Studi di Napoli Federico II, Italy
  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy
  • Cristina Trombetti

    Università degli Studi di Napoli Federico II, Italy
On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets cover
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Abstract

Let be an open convex set in with finite width, and with boundary . Let be the torsion function for , i.e., the solution of . An upper bound is obtained for the product of , where is the bottom of the spectrum of the Dirichlet Laplacian acting in . The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area , it is shown that , and that this bound is sharp.

Cite this article

Michiel van den Berg, Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti, On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 2091–2105

DOI 10.4171/RMI/1192