Abstract:Consider the Poincaré-Sobolev inequality on the hyperbolic space: for every n ≥ 3 and 1 < p ≤ n+2 n−2 , there exists a best constant S n,p,λ (B n ) > 0 such that, where (n−1) 2
4is the bottom of the L 2 -spectrum of −∆ B n . It is known from the results of Mancini and Sandeep [56] that under appropriate assumptions on n, p and λ there exists an optimizer, unique up to the hyperbolic isometries, attaining the best constant S n,p,λ (B n ). In this article we investigate the quantitative gradient stability of th… Show more
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