Neck Detection for Two-Convex Hypersurfaces Embedded in Euclidean Space undergoing Brendle-Huisken G-Flow

2018/03/27 by Majchrowski, Alexander
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.09878

Abstract

Recently Brendle-Huisken introduced a fully nonlinear flow G. Their aim was to extend the surgery algorithm of Huisken-Sinestrari, into the Riemannian setting. The aim of this paper is to go through the details on how to perform neck detection for a closed, embedded hypersurface M₀ in ℝⁿ⁺¹ undergoing this G-flow. In order to do this we make some adjustments to Brendle and Huiskens gradient estimate, after we have done this we can go on to argue as in Huisken-Sinestrari's paper Mean curvature flow with surgeries of two-convex hyperusrfaces, in order to classify two-convex surfaces undergoing G-flow.

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