Higher order geometric flow of hypersurfaces in a Riemannian manifold

2018/02/01 by Zonglin Jia, Jia, Zonglin, Youde Wang +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1802.00131

Abstract

In this paper, we consider the high order geometric flows of a submanifolds M in a complete Riemannian manifold N with dim(N)=dim(M)+1=n+1, which were introduced by Mantegazza in the case the ambient space is an Euclidean space, and extend some results due to Mantegazza to the present situation under some assumptions on N. Precisely, we show that if m∈ℕ is strictly larger than the integer part of n/2 and φ(t) is a immersion for all t∈[0,T) and if \mathfrakF_m(φ₀) is bounded by a constant which relies on the injectivity radius R>0 and sectional curvature K_π(K_π\leqslant1) of N , then T must be ∞.

Citations

• Minimal Varieties in Riemannian Manifolds

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