2018/09/15 by Chen, Bang-Yen, Wei, Shihshu Walter
#31B05 #53C21 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.05737
By applying an average method in PDE, we obtain a dichotomy between "constancy" and "infinity" of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold N1×f2 N2 × ⋯ × fk Nk into a Riemannian manifold. Generalizing the earlier work of the authors in [Glasg. Math. J. 51 (2009) 579-592], we establish sharp inequalities between the mean curvature of the immersion and the sectional curvatures of the ambient manifold under the influence of quantities of a purely analytic nature (the growth of the warping functions). Several applications of our growth estimates are also presented.