The Lp-Minkowski problem for −n < p < 1

Abstract Chou and Wang's existence result for the L p -Minkowski problem on S n − 1 for p ∈ ( − n , 1 ) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p ∈ ( 0 , 1 ) .