An asymptotic property of Huisken's functional on minimal submanifolds of Euclidean space

TL;DR

This paper investigates the long-term behavior of Huisken's functional on minimal submanifolds in Euclidean space, establishing that its limit equals the extrinsic asymptotic volume ratio, revealing a key geometric property.

Contribution

It proves that Huisken's functional converges to the extrinsic asymptotic volume ratio on minimal submanifolds in Euclidean space, providing new insight into their geometric analysis.

Findings

Huisken's functional limit equals the extrinsic asymptotic volume ratio

The result applies specifically to minimal submanifolds in Euclidean space

Provides a new asymptotic characterization of minimal submanifolds

Abstract

In this short note, we study the asymptotic property of Huisken's functional for mean curvature flow on the minimal submanifolds of Euclidean space. We prove that the limit of Huisken's functional equals to the extrinsic asymptotic volume ratio on the minimal submanifold of Euclidean space.