Stability for $ \Phi_{S, F,H} $ harmonic map and $ \Phi_{T, F,H} $ harmonic map

TL;DR

This paper investigates the stability properties of specific types of harmonic maps, namely $ ilde{ ext{Phi}}_{S, F,H} $ and $ ilde{ ext{Phi}}_{T, F,H} $, between or into $ ilde{ ext{Phi}} $-SSU manifolds, with a focus on compact convex hypersurfaces.

Contribution

It provides new theorems characterizing when these harmonic maps are stable or unstable in the context of $ ilde{ ext{Phi}} $-SSU manifolds and convex hypersurfaces.

Findings

Identifies conditions for stability and instability of the harmonic maps.

Provides criteria for $ ilde{ ext{Phi}}_{S, F,H} $-stability.

Establishes theorems relating manifold properties to harmonic map stability.

Abstract

In this paper, we mainly consider the stability of $ \Phi_{S, F,H} $ harmonic map and $ \Phi_{T,F,H} $ harmonic map from or into $ \Phi $-SSU manifold. We mainly consider the stability of $ \Phi_{S, F,H} $ harmonic map and $ \Phi_{T,F,H} $ harmonic map from or into compact convex hypersurface. We also give some Theorems to know when a manifold is $ \Phi_{S, F,H} $ -stable or $ \Phi_{S, F,H} $ -unstable.