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摘要
In this paper, we consider general harmonic measures mu(n,beta)(x) on the unit sphere Sn-1 in R-n, where x is an element of R-n with 0 <= vertical bar x vertical bar < 1, beta is an element of R and n >= 3. Following the idea in Barthe et al. (2014), we obtain the lower bound for the spectral gap of mu(n,beta)(x). For the harmonic measure (beta = 0), we improve the lower bound of the spectral gap in Barthe et al. (2014) and we also improve those in Milman (2015) for general beta is an element of R.
