Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
Simon Brendle, Kyeongsu Choi
Abstract
In this paper, we consider noncompact ancient solutions to the mean curvature flow in $\mathbb{R}^{n+1}$ ($n \geq 3$) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.
Topics & Concepts
MathematicsUniquenessRegular polygonMean curvature flowCurvatureFlow (mathematics)Convex bodyPure mathematicsMathematical analysisConvex curveCombinatoricsGeometryMean curvatureConvex hullGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsGeometry and complex manifolds