Proof of the Payne-pólya-weinberger Conjecture

  title={Proof of the Payne-pólya-weinberger Conjecture},
  author={MARK S. ASHBAUGH and Rafael D. Benguria},
In 1955 and 1956 Payne, Pólya, and Weinberger considered the problem of bounding ratios of eigenvalues for homogeneous membranes of arbitrary shape [PPW1, PPW2]. Among other things, they showed that the ratio k2IK °f * ^ r s t t w o eigenvalues was less than or equal to 3 and went on to conjecture that the optimal upper bound for A2/Aj was its value for the disk, approximately 2.539. It is this conjecture which we establish below. Since 1956 various authors have attempted to prove the… CONTINUE READING

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