This book is an introduction to the subject of mean curvature flow of hypersurfaces with
special emphasis on the analysis of singularities. This flow occurs in the description of the …

Mean Curvature Flow in Higher Codimension: Introduction and Survey Page 1 Mean
Curvature Flow in Higher Codimension: Introduction and Survey Knut Smoczyk Abstract In this …

In this paper, we show that if the Laplacian and gradient of the warping function of a compact
warped product submanifold Ωp+ q in the hyperbolic space ℍm (− 1) satisfy various extrinsic …

The study of the mean curvature flow from the perspective of partial differential equations
began with Gerhard Huisken's pioneering work in 1984. Since that time, the mean curvature …

Uniqueness of conical singularities for mean curvature flows - ScienceDirect Skip to main
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Let M be an n-dimensional submanifold in the simply connected space form F n+ p (c) with
c+ H 2> 0, where H is the mean curvature of M. We verify that if M n (n≥ 3) is an oriented …

In this paper, we investigate motion by mean curvature using the Allen–Cahn (AC) equation
in two and three space dimensions. We use an unconditionally stable hybrid numerical …

Protection against the consequences of Pyroclastic Density Currents (PDCs) is almost
impossible due to their high velocity, temperature, sediment load and mobility. PDCs …

Some new differentiable sphere theorems are obtained via the Ricci flow and stable
currents. We prove that if Mn is a compact manifold whose normalized scalar curvature and …

We prove rigidity theorems for ancient solutions of geometric flows of immersed
submanifolds. Specifically, we find pinching conditions on the second fundamental form that …