A splitting theorem for the weighted measure

Let M be an n -dimensional complete noncompact Riemannian manifold, h be a smooth function on M and d μ  =  e h d V be the weighted measure. In this article, we prove that when the spectrum of the weighted Laplacian has a positive lower bound λ 1 ( M ) > 0 and the m ( m  >  n )-dimensional Bak...

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