I am wondering if one can obtain a lower bound for the principal eigenvalue of laplacian on a closed manifold in terms of its volume. If this does not hold in general, would there be some special manifold where such bound exist? For example this is certainly true for $S^1,$ but I guess something could go weird in higher dimension.
2026-04-01 12:01:13.1775044873
lower bound for the principal eigenvalue of laplacian in terms of volume
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