Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone

TL;DR

This paper derives and proves the existence of unique self-expanding solutions to the mean curvature flow based on the generalized Lawson-Osserman cone, expanding understanding of geometric flow behaviors.

Contribution

It introduces a new class of self-expanders for mean curvature flow derived from the generalized Lawson-Osserman cone, with a proof of their existence and uniqueness under certain conditions.

Findings

Existence of self-expanders based on the generalized Lawson-Osserman cone.

Uniqueness of these self-expanders under local assumptions.

Development of a modified equilibrium theory for autonomous systems.

Abstract

We derive the equation of self-similar solutions to mean curvature flow based on the generalized Lawson-Osserman cone and prove the existence of self-expanders by modifying the theory of equilibria in the autonomous system. In particular, those self-expanders are unique if a local assumption is given.