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[2111.07719] Eigenvalue ratios for vibrating String equations with concave densities

https://arxiv.org/abs/2111.07719
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2026-07-25 09:43:02
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Text Highlight2026-07-25 13:04:02
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"arXivLabs: experimental projects with community collaborators"
Whisper Note
Wish more platforms did this, collaborative experiments are the future.
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Text Highlight2026-07-25 12:55:02
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"arXivLabs: experimental projects with community collaborators"
Whisper Note
So this is where they test the wild ideas before they go mainstream?
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Text Highlight2026-07-25 10:01:02
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"optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string"
Whisper Note
Huang's method again—that trick with zeros of eigenfunctions is really neat.
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Text Highlight2026-07-25 09:52:02
Original Highlight Excerpt
"optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string"
Whisper Note
I've seen this ratio before for constant density, but concave makes it way more interesting.
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arxiv.org
Text Highlight2026-07-25 09:43:02
Original Highlight Excerpt
"optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string"
Whisper Note
So the bound is optimal only when the density is concave—that's a pretty strong condition.

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