On the Invariant Spectrum of S 1 -Invariant Metrics on S 2

On the Invariant Spectrum of S−invariant Metrics on S

A theorem of J. Hersch (1970) states that for any smooth metric on S2, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S1-action on S2, one can restrict the Laplace operator to the subspace of S1-invariant functions and c...

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On the Invariant Spectrum of S1−invariant Metrics on S

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...

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ar X iv : m at h / 99 09 18 1 v 2 [ m at h . SP ] 1 1 O ct 1 99 9 ON THE INVARIANT SPECTRUM OF S 1 − INVARIANT METRICS ON S

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...

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ar X iv : m at h / 99 09 18 1 v 3 [ m at h . SP ] 3 1 O ct 2 00 1 ON THE INVARIANT SPECTRUM OF S 1 − INVARIANT METRICS ON S

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...

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ar X iv : m at h / 99 09 18 1 v 1 [ m at h . SP ] 3 0 Se p 19 99 ON THE INVARIANT SPECTRUM OF S 1 − INVARIANT METRICS ON S

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...

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On the Invariant Spectrum of S 1 -Invariant Metrics on S 2

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On the Invariant Spectrum of S−invariant Metrics on S