On the inverse mean curvature flow in warped product manifolds

2016/10/17 by Mullins, Thomas
#35K55 #53C21 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.05234

Abstract

We consider the warped product manifold, ℝ₊ ×_\bfId Mⁿ, with Riemannian metric γ≡ d r² ⊕ r² σ, where (Mⁿ, σ) is a smooth closed Riemannian n-manifold. We investigate what sufficient curvature condition is required of σ to ensure that a solution to the inverse mean curvature flow - commencing with a star-shaped surface - exists for all times t>0.

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