Existence of monotone Morse flow lines of the expander functional

Key Points

• This research aims to construct a Morse flow line connecting a strictly unstable self-expander to a stable one.
• Constructed singular Morse flow line of the expander functional.
• Analyzed properties of monotonicity in the flow.
• Explored stability and instability within asymptotically conical self-expanders.
• Successfully demonstrated the existence of a monotone Morse flow line.
• Identified a small singular set within the constructed flow.
• Connected strictly unstable and stable self-expanders.