A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle
Duke Mathematical Journal 135(1) (2006) 181--202 We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: on the Klein bottle $\mathbb{K}$, the metric of revolution $$g_0= {9+ (1+8\cos ^2v)^2\over 1+8\cos ^2v} (du^2 + {dv^2\over 1+8\cos ^2v}),$$ $0\...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | Duke Mathematical Journal 135(1) (2006) 181--202 We prove the following conjecture recently formulated by Jakobson,
Nadirashvili and Polterovich \cite{JNP}: on the Klein bottle $\mathbb{K}$, the
metric of revolution $$g_0= {9+ (1+8\cos ^2v)^2\over 1+8\cos ^2v} (du^2 +
{dv^2\over 1+8\cos ^2v}),$$ $0\le u |
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| DOI: | 10.48550/arxiv.math/0701773 |