Universal eigenvalue ratio conjecture for weighted compact Alexandrov spaces
Universal eigenvalue ratio conjecture for weighted compact Alexandrov spaces
Let be a weighted compact finite-dimensional Alexandrov space of , and let be a natural number. Eigenvalue ratio conjecture. There exists a universal constant such that
This conjecture proposes a uniform upper bound on the ratio of consecutive Laplacian eigenvalues in this class of metric-measure spaces. The supplied source does not indicate whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Kei Funano, “Estimates of eigenvalues of Laplacian by a reduced number of subsets”, arXiv:1601.07581 (2016).
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