On negatively curved spaces in dimensions 2 and 3, sufficiently small clamped plates have fundamental tone at least that of a hyperbolic ball of the same volume, yielding a McKean-type spectral gap.
Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen.Jber
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Fundamental tones of clamped plates in nonpositively curved spaces
On negatively curved spaces in dimensions 2 and 3, sufficiently small clamped plates have fundamental tone at least that of a hyperbolic ball of the same volume, yielding a McKean-type spectral gap.