Abstract
the operator LD1gC aC bK g on a complete noncompact surface .M 2 ; g/. Assuming that L is nonnegative for some constants a > 0 and b > 1=4, we show that the infimum of the spectrum of M 2 is bounded from above by a=.4b 1/. We apply this result to stable minimal surfaces immersed into homogeneous 3-manifolds.
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